Fact-checked by Grok 2 weeks ago

Put option

A put option is a type of derivative contract in financial markets that grants the holder the right, but not the obligation, to sell an underlying asset—such as stocks, bonds, commodities, or indices—at a predetermined price, known as the strike price, on or before a specified expiration date.^[1] This instrument derives its value from the underlying asset and is typically traded on exchanges like the Chicago Board Options Exchange (CBOE).^[2] Put options serve two primary functions in investment strategies: hedging and speculation.^[3] For hedging, investors who own the underlying asset can purchase put options to protect against potential price declines, effectively setting a floor on losses; if the asset's market price falls below the strike price, the option allows the holder to sell at the higher strike price, offsetting the decline.^[1] In speculative trading, buyers of put options anticipate a drop in the underlying asset's price and can profit from the difference between the strike price and the lower market price upon exercise, minus the premium paid for the option.^[3] The premium, which is the cost of acquiring the option, is influenced by factors such as the underlying asset's volatility, time until expiration, interest rates, and the difference between the current market price and the strike price.^[3] Unlike call options, which provide the right to buy an asset, put options are bearish instruments that gain value as the underlying asset's price decreases.^[2] Options can be American-style, exercisable at any time before expiration, or European-style, exercisable only at expiration, with the style depending on the contract specifications set by exchanges and regulators like the U.S. Securities and Exchange Commission (SEC) and the Commodity Futures Trading Commission (CFTC).^[1] Trading put options involves risks, including the potential loss of the entire premium if the option expires worthless, and requires approval from brokers due to the leverage and complexity involved.^[1]

Fundamentals

Definition

A put option is a financial derivative contract that grants the holder the right, but not the obligation, to sell a specified underlying asset at a predetermined price, known as the strike price, on or before a designated expiration date.^[4] This instrument derives its value from the underlying asset, which can include equities such as individual stocks or broader market indices.^[5] The expiration date serves as a critical prerequisite, marking the end of the period during which the holder may choose to exercise the option, after which it becomes worthless if not exercised.^[6] In a put option transaction, the buyer acquires this right by paying a premium to the seller, who in turn assumes the obligation to purchase the underlying asset at the strike price should the buyer exercise the option.^[7] This asymmetry defines the core rights and obligations: the buyer benefits from potential downside protection or profit if the asset's price falls below the strike, while the seller collects the premium but faces the risk of having to buy the asset at an above-market price upon exercise.^[8] The origins of options trading trace back to the 17th century in Dutch commerce, where contracts resembling puts and calls were traded on the Amsterdam bourse, particularly for shares of the Dutch East India Company to manage trade risks. However, modern standardized put options emerged in the United States with the establishment of the Chicago Board Options Exchange (CBOE) in 1973, which initially listed call options before introducing put options in 1977, facilitating centralized, regulated trading on exchanges.^[9] As the inverse of a call option—which provides the right to buy—a put option enables holders to hedge against or speculate on declining asset prices.^[4]

Key Features

A put option's strike price represents the predetermined price at which the holder has the right to sell the underlying asset to the writer upon exercise.^[10] This fixed price serves as the reference point for determining the option's value relative to the current market price of the asset.^[10] The expiration date specifies the last day on which the put option can be exercised, after which the contract becomes void if not exercised or sold.^[11] As this date approaches, the option experiences time decay, known as theta, which erodes the option's extrinsic value at an accelerating rate, particularly for out-of-the-money puts.^[12] For instance, a put option with 30 days to expiration might lose value more slowly initially but decay more rapidly in the final weeks, reflecting the diminishing probability of the underlying asset's price falling below the strike.^[13] The premium is the upfront payment made by the put option buyer to the seller, representing the cost of acquiring the right to sell the underlying asset.^[14] This non-refundable amount compensates the seller for the obligation and is influenced by factors such as the strike price, expiration date, and current market conditions.^[14] Put options come in two primary exercise styles: American and European. American-style puts, common for equity options, can be exercised by the holder at any time on or before the expiration date.^[15] For example, if the underlying stock price drops significantly below the strike before expiration, the holder might exercise an American put early to sell the shares immediately and capture the intrinsic value, especially if interest rates make holding cash advantageous.^[15] In contrast, European-style puts, typical for index options, can only be exercised on the expiration date itself.^[16] For instance, a European put on an index would require the holder to wait until expiration; if the index level is below the strike at that point, exercise occurs, but early action is impossible even if the index falls sharply beforehand.^[16] Settlement of exercised put options occurs either through physical delivery or cash payment, depending on the underlying asset. Physical delivery, standard for equity put options, involves the holder delivering the underlying shares to the writer in exchange for the strike price times the number of shares per contract.^[17] Cash settlement, prevalent for index put options, results in a monetary payment equal to the difference between the strike price and the index settlement value, multiplied by the contract's multiplier, without any asset transfer.^[18] Put options are available on various underlying assets, such as equities, indices, and commodities. Moneyness describes the relationship between the put option's strike price and the current price of the underlying asset, categorizing options as in-the-money (ITM), at-the-money (ATM), or out-of-the-money (OTM). A put is ITM when the strike price exceeds the current underlying price, providing immediate intrinsic value if exercised.^[19] It is ATM when the strike equals the current price, with no intrinsic value but potential time value.^[20] An OTM put has a strike below the current price, offering no intrinsic value and relying solely on time value for any premium.^[20]

Payoff and Valuation

Payoff Profile

The payoff of a long put option at expiration is determined by the difference between the strike price K and the underlying asset's price S_T, if positive, minus the premium paid c to acquire the option. Mathematically, this is expressed as \max(K - S_T, 0) - c.^[21] This formula captures the option's intrinsic value at expiration, providing the holder with the right to sell the underlying asset at the strike price if it is advantageous, resulting in a profit only if the underlying price falls sufficiently below the strike to offset the premium. The payoff diagram for a long put position exhibits a characteristic hockey-stick shape, with the horizontal portion representing losses limited to the premium paid when the underlying price exceeds the strike, and the vertical portion illustrating unlimited potential gains as the underlying price declines below the strike.^[22] This structure highlights the asymmetric risk profile: the maximum loss is capped at the premium, while downside protection extends indefinitely, making it a tool for hedging against adverse price movements in the underlying asset. The breakeven point for a long put occurs at K - c, where the underlying price at expiration equals the strike minus the premium, such that any further decline yields a profit.^[21] At expiration, the put option's value consists solely of its intrinsic value \max(K - S_T, 0), as the time value component, which accounts for the potential for future price movements, diminishes to zero.^[3] For a short put position, the payoff at expiration is the negative of the long put's intrinsic value plus the premium received c, formulated as c - \max(K - S_T, 0).^[23] This reflects the writer's obligation to buy the underlying at the strike if exercised, with profits limited to the premium if the option expires worthless (when S_T \geq K), but potential losses increasing linearly as the underlying price drops below the strike. American put options, unlike European puts, allow early exercise, which may be optimal near expiration if the option is deeply in-the-money, as the holder can capture the intrinsic value and earn interest on the strike price proceeds sooner than waiting.^[24] This early exercise premium arises because the continuation value may be less than the intrinsic value for deep in-the-money American puts, incentivizing exercise to avoid opportunity costs associated with holding the option.^[25]

Pricing Methods

The pricing of put options involves determining their fair value prior to expiration using mathematical models that account for the underlying asset's dynamics under assumptions of efficient markets and no arbitrage. These methods extend beyond the intrinsic value at expiration by incorporating time value, volatility, and other market factors. The most widely adopted approaches include closed-form solutions for European-style puts and numerical methods for American-style puts, which allow for early exercise. For European put options, which cannot be exercised before expiration, the Black-Scholes model provides a seminal closed-form formula assuming constant volatility, no dividends (q=0), and lognormal asset price distribution. The put price P is given by:

P = K e^{-rT} N(-d_2) - S N(-d_1)

where S is the current spot price of the underlying asset, K is the strike price, r is the risk-free interest rate, T is the time to expiration, \sigma is the volatility of the underlying asset's returns, N(\cdot) is the cumulative distribution function of the standard normal distribution, d_1 = \frac{\ln(S/K) + (r + \sigma^2/2)T}{\sigma \sqrt{T}}, and d_2 = d_1 - \sigma \sqrt{T}. This formula, derived via a risk-neutral hedging argument, prices the put as the discounted expected payoff under the risk-neutral measure. A generalization by Merton incorporates continuous dividend yield q, replacing S with S e^{-qT} in the second term and adjusting d_1 to include (r - q + \sigma^2/2)T. The binomial model, suitable for American put options that permit early exercise, employs a discrete-time lattice to approximate the continuous process of the Black-Scholes framework. In this approach, the underlying price evolves over n periods in a recombining binomial tree, moving up by factor u or down by d at each step, calibrated such that the mean and variance match the lognormal distribution (e.g., u = e^{\sigma \sqrt{\Delta t}}, d = 1/u, where \Delta t = T/n). Option values are computed via backward induction: at expiration, the put payoff is \max(K - S_T, 0); at each prior node, the value is the maximum of the exercise value K - S and the discounted expected continuation value under the risk-neutral probability p = (e^{r \Delta t} - d)/(u - d). This method captures the early exercise premium for American puts, particularly when deep in-the-money, as higher interest rates or dividends can make immediate exercise optimal. Several key factors influence put option prices within these models. Implied volatility \sigma, solved inversely from the Black-Scholes formula to match observed market prices, directly increases put values by enhancing the probability of large downward moves in the underlying. Higher interest rates r decrease put prices, as the present value of the strike K e^{-rT} falls, reducing the option's expected payoff. Conversely, higher dividend yields q increase put prices by lowering the expected future spot price through ex-dividend drops. Other inputs like longer T amplify time value, while a lower S relative to K boosts intrinsic value. The sensitivities of put prices to these inputs are quantified by the option Greeks, derived as partial derivatives of the Black-Scholes formula. Delta (\Delta) measures price sensitivity to S and is negative for puts, ranging from 0 (out-of-the-money) to -1 (deep in-the-money), indicating an inverse relationship. Gamma (\Gamma) is positive and identical to that of the equivalent call, reflecting convexity in price changes. Vega (\nu) is positive, showing that higher \sigma raises the put value. Theta (\Theta) is typically negative, capturing time decay that erodes the option's extrinsic value as expiration nears. Rho (\rho) is negative, as rising r diminishes put attractiveness. Put-call parity provides a model-independent relation to derive put prices from equivalent calls, ensuring no-arbitrage consistency for European options: C - P = S e^{-qT} - K e^{-rT}, or P = C - S e^{-qT} + K e^{-rT} with no dividends (q=0). This equation holds under frictionless markets and allows synthetic replication of puts using calls, the underlying, and risk-free borrowing.

Trading Mechanics

Buying Puts

Buying a put option grants the buyer the right, but not the obligation, to sell a specified quantity of the underlying asset—typically 100 shares of stock—at a predetermined strike price on or before the option's expiration date, in exchange for paying a premium to the seller upfront. This process allows the buyer to secure this right without needing to own the underlying asset, distinguishing it from direct short selling. The premium reflects the market's assessment of the option's value, influenced by factors such as the underlying asset's current price, time to expiration, and volatility, though the buyer pays it in full at purchase. Investors are motivated to buy put options primarily for bearish speculation, anticipating a decline in the underlying asset's price to generate profits by exercising the option or selling it at a higher value before expiration. Alternatively, puts serve as downside protection for existing long positions in the underlying asset, limiting potential losses if the market moves adversely, though this standalone purchase focuses on the mechanics rather than integrated portfolio strategies. The strategy appeals to those seeking leveraged exposure to price drops without the unlimited risk of shorting the asset directly. The buyer's risk is strictly limited, with the maximum loss equal to the premium paid, which occurs if the underlying asset's price remains above the strike price at expiration, rendering the option worthless. In contrast, the maximum potential gain is theoretically the strike price minus the premium paid, realized if the underlying asset's price falls to zero, though in practice, gains are substantial during sharp declines as the option's value increases. The breakeven point at expiration is the strike price minus the premium, below which the position becomes profitable. For example, consider an investor buying one put option contract on stock XYZ, with a strike price of $50 and a premium of $3 per share (total cost $300 for 100 shares), when XYZ trades at $52. At expiration, if XYZ closes at $40, the buyer can exercise to sell at $50, netting a profit of $7 per share ($50 - $40 - $3) or $700 total. If XYZ closes at $45, the profit is $2 per share ($50 - $45 - $3) after the premium. However, if XYZ closes at $52 or higher, the option expires worthless, resulting in a $300 loss limited to the premium. Unlike option sellers, buyers face no margin requirements, as the transaction is fully paid by the premium, avoiding the need for collateral or ongoing maintenance to cover potential obligations. Additionally, there is no assignment risk for put buyers, since they alone decide whether to exercise the option and cannot be forced to fulfill any seller duties.

Selling Puts

Selling put options, also known as writing puts, involves the seller receiving an upfront premium from the buyer in exchange for assuming the obligation to purchase the underlying asset at the specified strike price if the option is exercised by the buyer.^[26] This process typically occurs through a brokerage account approved for options trading, where the seller opens a short position in the put contract, which represents 100 shares of the underlying asset per contract.^[3] Sellers are often motivated by the desire to generate income from the premium collected, particularly in neutral to bullish market outlooks where they anticipate the underlying asset's price will remain above the strike price at expiration, allowing the option to expire worthless.^[27] Alternatively, sellers with a bullish view may use this strategy to potentially acquire the asset at a net discounted price (strike minus premium) if assigned, effectively positioning themselves to buy shares they deem undervalued.^[26] The maximum gain for the seller is limited to the premium received, as the position profits fully if the option expires worthless.^[28] However, the maximum loss is substantial and occurs if the underlying asset's price falls to zero, resulting in a net loss equal to the strike price minus the premium received (multiplied by the contract size).^[26] For example, consider selling one put option on XYZ stock with a strike price of $50 for a premium of $3 per share ($300 total for 100 shares). If XYZ closes above $50 at expiration, the option expires worthless, and the seller keeps the full $300 premium as profit. If XYZ falls below $50, the buyer may exercise, obligating the seller to buy 100 shares at $50 each ($5,000 total), resulting in an immediate unrealized loss offset only by the $300 premium; further declines in XYZ's price would amplify the loss.^[26] Selling uncovered (naked) puts requires a margin account, with initial and maintenance margin typically calculated as 100% of the option premium received plus 20% of the underlying asset's value, minus any out-of-the-money amount, subject to a minimum of 10% of the strike price.^[29] As an alternative, cash-secured puts involve setting aside the full cash amount needed to purchase the underlying asset at the strike price (e.g., $5,000 for the $50 strike example), which fully collateralizes the position without relying on margin borrowing.^[30]^[31] For American-style put options, which can be exercised at any time before expiration, sellers face the risk of early assignment, particularly if the option becomes deeply in-the-money or in anticipation of events like dividends on the underlying stock, though such assignments are relatively uncommon for puts compared to calls.^[32]^[33] The breakeven point for the seller is the strike price minus the premium received.^[26]

Strategies and Applications

Hedging Applications

Put options serve as a key instrument for portfolio insurance, enabling investors to limit downside risk on equity holdings without liquidating positions. In the protective put strategy, an investor maintains a long position in the underlying stock while simultaneously purchasing put options on the same shares, effectively capping potential losses at the put's strike price minus the premium paid. This approach functions like insurance, providing the right to sell the stock at the predetermined strike if prices decline, while allowing unlimited upside participation if the market rises. For instance, if an investor holds shares trading at $100 and buys a put with a $95 strike for a $3 premium, the maximum loss is restricted to $8 per share (the difference between purchase price and strike, plus premium), regardless of further declines.^[34]^[35] Market makers and institutions also employ put options in delta hedging to neutralize directional risk in their options portfolios. Delta measures an option's sensitivity to changes in the underlying asset's price, and for puts, it is negative, meaning the option's value rises as the asset falls. By buying or selling puts alongside the underlying security, market makers adjust their overall portfolio delta to zero, mitigating exposure to small price movements and focusing risk on higher-order Greeks like gamma or vega. This dynamic process involves frequent rebalancing, often using puts to offset positive delta from sold calls or other positions, ensuring the hedged portfolio earns a risk-free return in theory under the Black-Scholes framework.^[36]^[37] Broad market protection is commonly achieved through index put options, such as those on the S&P 500, particularly during periods of heightened volatility. During the 2008 financial crisis, demand for out-of-the-money (OTM) S&P 500 puts surged as investors sought to hedge against the index's 56% drawdown, with net purchases rising sharply from 2007 onward to counter escalating tail risks. Similarly, in the 2020 COVID-19 market crash, which saw the S&P 500 plummet over 30% in a month, put options provided critical downside buffers, with hedging costs spiking to 2.5-6% of the index value for one-month OTM protection. These examples illustrate how index puts enable efficient, diversified hedging for large portfolios without targeting individual stocks.^[38]^[39]^[40] The primary cost of put-based hedging is the option premium, which acts as the insurance expense and erodes returns if the market remains stable or rises. Investors often select OTM strikes—below the current price—to reduce this cost, trading some protection level for affordability; for example, a put 5-10% OTM might cost 1-2% of the underlying value annually, compared to at-the-money options at 3-5%. In the U.S., straddle rules apply to offsetting positions involving puts, deferring recognition of losses until all positions are closed, which can affect the timing of tax offsets. However, over-hedging poses limitations, as excessive put coverage can lead to opportunity costs during bull markets, where premiums paid represent forgone gains without corresponding protection benefits, potentially underperforming unhedged benchmarks over long horizons.^[41]^[42]^[43]^[44]

Speculative Strategies

Speculative strategies with put options involve aggressive positions designed to capitalize on anticipated declines in the underlying asset's price, leveraging the option's asymmetric payoff to achieve high reward-to-risk ratios. One common approach is the purchase of put options, where an investor buys puts without holding any offsetting position in the underlying security or other options, allowing for a pure bearish bet with limited downside risk equal to the premium paid.^[45] This strategy provides significant leverage, as the buyer controls a large notional amount of the underlying for a fraction of its value, potentially yielding substantial profits if the asset price falls sharply below the strike.^[46] More advanced speculative setups include put ratio backspreads, which amplify downside gains by buying a greater number of out-of-the-money (OTM) puts than the in-the-money (ITM) puts sold, typically in a 2:1 ratio.^[47] For instance, selling one ITM put and buying two OTM puts creates a net debit position with unlimited profit potential on a significant price drop, while the sold put offsets some cost but caps upside risk if the market rises moderately.^[48] This structure suits traders expecting a strong bearish move, as the excess long puts benefit disproportionately from large declines.^[49] Put options also feature prominently in volatility trading, where long positions profit from spikes in implied volatility, particularly around event-driven catalysts like earnings announcements.^[46] As implied volatility rises, the extrinsic value of the put increases due to heightened uncertainty, boosting the option's price even if the underlying remains stable; this vega sensitivity makes long puts ideal for speculating on volatility expansions prior to high-impact events.^[50] A representative example of such speculation involves betting on a technology stock's decline before its earnings report by purchasing at-the-money (ATM) puts. For a stock trading at $100, buying one put contract (controlling 100 shares, or $10,000 notional) might cost a $5 premium per share, totaling $500, providing leveraged exposure to a potential drop without committing the full underlying value. If the stock falls 10% post-earnings, the put could double in value, yielding a high return on the modest initial outlay, though the entire premium is lost if the stock rises or stays flat.^[46] Effective risk management in these strategies emphasizes position sizing, where traders allocate no more than 1-2% of their total account equity to any single trade to limit drawdowns from adverse moves.^[51] This approach preserves capital across multiple speculative attempts, ensuring that even a string of losses does not cripple the portfolio.^[52] In the United States, frequent speculative trading with put options may trigger regulatory oversight under the pattern day trader (PDT) rule enforced by the Financial Industry Regulatory Authority (FINRA). As of 2025, accounts executing four or more day trades—including options—within five business days, when such trades exceed 6% of total activity, must maintain at least $25,000 in equity to continue unrestricted day trading, though FINRA approved amendments in September 2025 to replace this with a risk-based intraday margin approach expected to take effect in 2026; otherwise, limitations on further trades apply.^[53]^[54]^[55]

Protective Uses

Protective put strategies often involve combining put options with underlying assets to limit downside risk while maintaining potential upside, particularly for individual investors seeking to safeguard specific holdings or income sources. One common approach is the collar strategy, which consists of holding a long position in the underlying stock, purchasing a put option for downside protection, and selling a call option with a higher strike price to offset the put's cost, effectively creating a zero-cost hedge. This structure caps both potential losses and gains, with the put providing a floor price for selling the stock and the call obligating sale if the price rises above its strike. For instance, an investor owning shares of a volatile stock might buy a put at a 10% below-market strike and sell a call at a 10% above-market strike, resulting in limited net premium outlay while reducing exposure to sharp declines.^[56]^[57] The married put strategy, also known as a protective put, entails the simultaneous purchase of a stock and a put option on that stock, immediately providing insurance against declines in the new position's value. This is particularly useful for investors entering a bullish position on a stock but wary of short-term volatility, as the put allows selling the stock at the strike price if it falls, while retaining unlimited upside if it rises. Unlike a covered call, the married put avoids capping gains and requires no margin, making it suitable for cash accounts. For example, buying 100 shares of a technology firm at $100 per share alongside a three-month put at a $95 strike ensures the position's value does not drop below $95 per share (minus the premium), preserving capital in a new investment. Empirical analyses confirm that married puts can replicate portfolio insurance effects, forming a lower bound for the combined position's value.^[58]^[59]^[60] Selling cash-secured puts on dividend-paying stocks is an income-generation strategy for investors interested in potentially acquiring shares at a discounted effective price, while collecting premiums to enhance yield. In this approach, an investor sells puts on high-dividend stocks they wish to own, using the premium to lower the breakeven purchase price; if the stock price stays above the strike at expiration, the put expires worthless, allowing premium retention and potential repetition for ongoing income. If assigned, the investor buys the shares below the current market (strike minus premium) and benefits from upcoming dividends. This method is especially appealing for stable, dividend aristocrats, as the premium can approximate 1-2% quarterly yield enhancement, though it risks ownership during downturns.^[61]^[62] For investors with international exposure, currency put options serve as a targeted hedge against adverse exchange rate movements, particularly for exporters receiving payments in foreign currencies. A U.S. exporter anticipating receipts in euros, for instance, might buy a put on the euro (or equivalently, a call on USD) to lock in a minimum USD conversion value, protecting income streams from euro depreciation. Similarly, non-U.S. exporters receiving USD payments could purchase USD puts to ensure a floor exchange rate into their home currency, mitigating losses if the USD weakens. This strategy retains upside if rates move favorably, as the put can expire unexercised, and is commonly layered with forwards for cost efficiency in volatile forex markets. Studies on corporate hedging highlight that such options reduce earnings volatility for firms with significant export revenues without fully sacrificing potential gains from currency appreciation.^[63]^[64]^[65] In retirement accounts like IRAs, put options offer a compliant way to implement downside protection without triggering margin requirements or borrowing restrictions inherent to taxable brokerage accounts. Investors can buy protective puts on held stocks or indices within an IRA to insure against market drops, preserving principal for long-term growth; for example, pairing an S&P 500 ETF with index puts creates a floor on portfolio value during retirement drawdown phases. This approach avoids the complexities of short-selling or leverage prohibited in IRAs, allowing tax-deferred hedging that aligns with conservative allocation shifts near retirement. Regulatory guidance from the Department of Labor affirms that such strategies, when used judiciously, support fiduciary standards by reducing volatility in participant accounts without excessive speculation.^[66]^[67]^[68]

References

[1]
Investor Bulletin: An Introduction to Options
Mar 18, 2015 · A put option is a contract that gives the buyer the right to sell shares of an underlying stock at the strike price for a specified period of ...
[2]
Futures Glossary | CFTC
A short call or put option position that is covered by the sale or purchase of the underlying futures contract or other underlying instrument. For example, in ...
[3]
Put Option: What It Is, How It Works, and How To Trade - Investopedia
A put option is a financial contract that comes with the right to sell a certain asset at a certain price, even if the market price is lower. The price for ...Protective Put · Call Option · Fixed price (strike price)Missing: authoritative source
[4]
The Facts About Options
Put: An option contract that gives the owner the right to sell the underlying security at a specified price (its strike price) for a certain, fixed period ( ...
[5]
The Creation of Listed Options at Cboe
Mar 1, 2024 · From its humble beginnings in 1973, Cboe, under the visionary leadership of Joe Sullivan, revolutionized the way options are traded.
[6]
[PDF] Rules of Cboe Exchange, Inc.
... Put. (n). The term “put” means an option contract under which the holder of the option has the right, in accordance with the terms and provisions of the option ...
[7]
[PDF] KEY INFORMATION DOCUMENT (Equity Index Options – Long Put)
A seller of a put option has a short position and has sold the right to sell the underlying asset to the buyer.
[8]
[PDF] KEY INFORMATION DOCUMENT (Equity Options – Short Put
Objectives. A put option gives a buyer the right but not the obligation to sell the underlying asset at a certain price (the strike price) at any.
[9]
CBOE Options Exchange Definition - Investopedia
The CBOE is an important options exchange based in Chicago, founded in 1973. · In 2010 the exchange incorporated as a holding company with the exchange as its ...
[10]
Understanding Option Strike Prices: Definition, Function, and Impact
The strike price is a key variable of call and put options. It defines at which price the option holder can buy or sell the underlying security, respectively.Missing: settlement | Show results with:settlement
[11]
What Happens When Options Expire? - Investopedia
Holding an option through the expiration date without selling doesn't guarantee profits, but may limit loss. Find out what happens when options expire.
[12]
Theta: What It Means in Options Trading, With Examples
Theta is also known as an option's time decay. It's the daily amount by which an option's value drops. Key Takeaways. An option will lose value as it ...What Is Theta? · How Theta Works · Time Decay and Values · The Four Greeks
[13]
Theta Decay in Options Trading: Strategies to Know | Charles Schwab
Jan 23, 2024 · (OTM) call options have strike prices above the underlying stock price, and OTM put options have strike prices below the stock price. At-the- ...
[14]
What Is Option Premium? Pricing Factors and Examples Explained
The moneyness affects the option's premium because it indicates how far away the underlying security price is from the specified strike price.Missing: settlement | Show results with:settlement
[15]
American Option Definition, Pros & Cons, Examples
### Summary: American vs. European Options for Puts (Exercise Styles)
[16]
European Options: Definition, Types, and Differences from American Options
### Summary of European Options Exercise for Puts
[17]
Options Disclosure Document
### Summary of Settlement Types for Put Options (Equities and Indices)
[18]
Equity vs. Index Options - The Options Industry Council
Equity options are physically settled with shares, while index options are cash-settled, using an index value times a multiplier, not specific shares.<|separator|>
[19]
When Is a Put Option Considered to Be "In the Money"? - Investopedia
May 31, 2025 · A put option is said to be in the money when the strike price is higher than the underlying security's market price. Investors commonly use put ...
[20]
Out of the Money: Option Basics and Examples - Investopedia
Apr 21, 2025 · In-The-Money (ITM): The strike price is favorable compared to the current market price and you could profit by exercising the option. · At-The- ...Missing: settlement | Show results with:settlement
[21]
Call & Put Option Payoff Charts + Formulas (CFA/FRM) - AnalystPrep
Aug 21, 2020 · Understand how to calculate call and put option payoffs with step-by-step examples, diagrams, and formulas. Ideal for CFA and FRM exam prep.Call Options · Put Options · Value at Expiration of a Put... · Short Put
[22]
Put Option Payoff Diagram and Formula - Macroption
Put Option Payoff Diagram and Formula · P/L per share = MAX ( strike price – underlying price , 0 ) – initial option price · P/L = ( MAX ( strike price – ...Put Option Payoff Diagram · Put Option Payoff Formula
[23]
Short Put Payoff Diagram and Formula - Macroption
Short put payoff per share = initial option price – MAX(0, strike price – underlying price) · Short put payoff = (initial option price – MAX(0, strike price – ...
[24]
Early Exercise of Put Options on Stocks
Aug 17, 2011 · ... Early Exercise of Put Options on Stocks (August 17, 2011). Journal of Finance, Forthcoming, Available at SSRN: https://ssrn.com/abstract=1911208 ...
[25]
Early exercise on American put - Forum | Bionic Turtle
Apr 12, 2013 · The early exercise of an American put option is attractive when the interest earned on the strike price is greater than the insurance element lost.
[26]
Introduction to Put Writing - Investopedia
Writing Puts to Buy Stock. The next use for writing put options to get long a stock at a discounted price. Instead of using the premium-collection ...
[27]
How To Gain From Selling Put Options in Any Market - Investopedia
Nov 20, 2024 · Selling (writing) a put option allows an investor to potentially own the underlying security at a future date and at a more favorable price.<|control11|><|separator|>
[28]
What Is a Naked (Uncovered or Short) Put and How Does It Work?
Naked Put: Selling put options without holding an ...
[29]
[PDF] Margin Manual - Cboe Global Markets
Further, broker-dealers require a minimum margin account equity well in excess of $2,000 for uncovered, short option transactions.
[30]
Cash-Secured Put - The Options Industry Council
There are two principal risks. First, the stock might not only dip but plummet well below the strike price. The investor must be comfortable with the strike ...Missing: mechanics | Show results with:mechanics
[31]
Understanding Option Margin: Definition, Requirements, and ...
Oct 23, 2025 · ... selling naked puts may require Level II clearances and a margin account. Level III and IV accounts often have lower margin requirements.What Is Option Margin? · Option Margin Fundamentals · Circumventing Margin...
[32]
Trading Options: Understanding Assignment
Only about 7% of options positions are typically exercised, but that does not imply that investors can expect to be assigned on only 7% of their short positions ...
[33]
Key Differences Between American and European Options Explained
A put option gives the owner the right to sell the stock. The upfront fee, called the premium, is what the investor pays to purchase the option.1. Stock ...Missing: moneyness | Show results with:moneyness
[34]
Protective Put Option Strategy - Fidelity Investments
A protective put position is created by buying (or owning) stock and buying put options on a share-for-share basis.
[35]
Understanding the protective put option strategy - Saxo
A protective put is a powerful tool for managing risk in your portfolio. It provides a financial safety net, much like insurance, by capping potential losses.
[36]
Delta Hedging - Menthor Q
Delta hedging is a risk management strategy commonly used in options trading to offset or minimize the directional risk associated with an options position.
[37]
[PDF] On Market-Making and Delta-Hedging
• Option positions can be hedged using delta-hedging. • Delta-hedged positions should expect to earn risk-free return. Page 9. Market Maker Risk. • Market ...
[38]
[PDF] The Supply and Demand of S&P 500 Put Options
2008 financial crisis. The net buy of OTM puts began rising in 2004 as the RN variance and disaster index began to fall, consistent with our model. In 2007 ...
[39]
Hedging Market Uncertainties in 2020 - WisdomTree
Mar 26, 2020 · Well, the stock market crashed. The S&P 500 reached bear market territory when it dropped to 2,702 on March 11. And so far, the pain hasn't ...
[40]
Hedged Equity: For the Best of Times, For the Worst of Times
During the 2020 Pandemic and the 2022 bear market it would cost anywhere between 2.5% to 6% of the S&P 500's value to purchase a one-month put option. During ...
[41]
Master Hedging With Put Options: Protect Your Portfolio - Investopedia
Other variations on put spreads include diagonal spreads, which involve buying and selling put options with different strike prices and expiration dates.<|control11|><|separator|>
[42]
Using S&P 500 Put Options to Hedge a Downturn - Charles Schwab
Aug 6, 2025 · Investors pay a premium to set up a protective put position. The size of the position depends on how much of the portfolio they want to hedge.
[43]
Understanding Tax Rules for Call and Put Options in the U.S.
Oct 13, 2025 · However, special rules apply for straddles and other hedging strategies where losses may be deferred until all related positions are closed.
[44]
Portfolio Protection: Challenges with Equity Put Options
May 24, 2021 · This paper focuses on investigating put options' use as protection from equity market drawdowns. We explore the challenges in hedging with put options.
[45]
What Are Naked Options: Naked Calls & Puts Explained | tastylive
A naked long put is an options trading strategy where an investor buys a put option contract without simultaneously holding a position in the underlying asset ( ...
[46]
Long Put: Definition, How It Works, Importance, and Trading
A long put benefits from increasing implied volatility. Higher volatility results in greater time value being priced into the put option. This causes the value ...
[47]
Put Backspread Guide [Setup, Entry, Adjustments, Exit] - Option Alpha
A put backspread is a multi-leg, risk-defined, bearish strategy with unlimited profit potential. The strategy looks to take advantage of a significant move down ...
[48]
Put Ratio Back spread – Varsity by Zerodha
The Put Ratio Back Spread is a 3 leg option strategy as it involves buying two OTM Put options and selling one ITM Put option. This is the classic 2:1 combo.
[49]
Back Spread w/Puts - The Options Playbook
A put ratio backspread is a very bullish seasoned option strategy involving the sell and buying of puts, at different strike prices, that expire in the same ...
[50]
Long Put Strategy: A Detailed Guide for Investors
Jan 16, 2025 · 2. Volatility Trading. Long puts are highly sensitive to implied volatility. Experienced traders may capitalize on anticipated volatility spikes ...
[51]
How To Reduce Risk With Optimal Position Size - Investopedia
Apr 22, 2025 · Position sizing transforms the abstract concept of risk management into concrete action—it's how you decide exactly how much capital to commit ...
[52]
Adjusting Position Size: Managing Risk Without Sacrificing Profit ...
Aug 20, 2025 · The key to avoiding these traps is strict risk management. Stick to the 1–2% rule: never risk more than 1–2% of your account on a single trade.
[53]
[PDF] Margin Rules for Day Trading | SEC.gov
FINRA rules define a pattern day trader as any customer who executes four or more “day trades” within five business days, provided that the number of day ...Missing: speculation | Show results with:speculation
[54]
Day Trading | FINRA.org
First, pattern day traders must maintain minimum equity of $25,000 in their margin account on any day that the customer day trades. This required minimum equity ...Missing: speculation | Show results with:speculation
[55]
[PDF] Lecture 6 Collars. Risk management using collars. - UT Math
A collar is a financial position consisting of: • the purchase of a put option and. • the sale of a call option with a higher strike price, with both options ...Missing: explanation | Show results with:explanation
[56]
[PDF] Financial Mathematics MATH 5870/6870Based on Robert L ...
Sep 1, 2021 · A collar is the purchase of a put option and the sale of a call option with a higher strike price, with both options having the same underlying ...
[57]
Commission Guidance on Rule 3b-3 and Married Put Transactions
Nov 21, 2003 · A married put is buying a put option to sell securities at a set price, bought with the same securities. The SEC guidance addresses how these ...
[58]
[PDF] The Equity Options Strategy Guide
In other words, one collar equals one long put and one written call along with owning 100 shares of the underlying stock. The primary concern in employing a ...Missing: explanation | Show results with:explanation
[59]
Option Portfolio Selection with Generalized Entropic Portfolio ... - NIH
2.2. A married put, or protective put option strategy involves adding a long-put position to a long stock position, forming a lower bound for the stock value. ...
[60]
[PDF] Lesser Known Option Trading Strategies
May 5, 2011 · The high dividend yield may be favored given qualified dividend tax treatment if the underlying security is acquired in the case of selling puts ...Missing: secured | Show results with:secured
[61]
Before you invest, you may want to review the YieldMax ... - SEC.gov
Alternatively, using an Options Strategy such as cash-secured put selling (selling put options while holding enough cash to purchase the Underlying Security ...
[62]
Giddy: Hedging Tools and Techniques - NYU Stern
In this article we consider the relative merits of several different tools for hedging exchange risk, including forwards, futures, debt, swaps and options.
[63]
[PDF] chapter vii currency risk management: options
The gain in the hedging position (put position) is: (1.60 - 1.50) USD/GBP * GBP 10,000 * 100 = USD 100,000. The premium keeps the investor from having a perfect ...
[64]
[PDF] Managing Currency Risks with Options - Montana State University
Collar Strategy – The concept of a long put hedge is very appealing to the extent that it provides limited downside risk while retaining at least a partial ...<|control11|><|separator|>
[65]
[PDF] Public Comment - U.S. Department of Labor
put options for downside protection. Viewed another way, this is is in the nature of "stock insurance. 99. EXAMPLE: IRA Investor owns 100 shares of Apple ...
[66]
[PDF] EBSA Subject: RIN 1210-AB32 - Public Comment
The puts ended up protecting me during the recent volatile down-draft in the market and my account balance went down by 1/3 less than it would have if I didn't ...
[67]
[PDF] Using Option Theory to Determine Optimal IRA Investment
The price (or income) of the put is fixed, therefore one will sell the put if the perceived value is less than the income from selling the option.Missing: downside protection
[68]
[PDF] PERFORMANCE ENHANCEMENT OF A STOCK INDEX ...
In general, collar strategies consist of purchasing a put option and selling a call option on an underlying asset (e.g. QQQQ) while also holding shares of the ...Missing: explanation | Show results with:explanation
[69]
Methods and Performances of Collar Strategies - Academia.edu
An equity portfolio with a collar strategy consists of a long position in the underlying index together with long put options for insurance and short call ...
[70]
[PDF] Risk Management Hedging Commodity Exposure
This strategy can be implemented through a collar option strategy where. Anheuser-Busch would sell put options with low strike prices (i.e X= 56) and buy ...