ARTIFICIAL INTELLIGENCE

“An out-of-the-money (OTM) option is an option contract that has no intrinsic value, meaning exercising it immediately would result in a loss, making it currently unprofitable but potentially profitable if the underlying asset’s price moves favorably before expiration.” – Out-of-the-money option

An out-of-the-money (OTM) option is an options contract that has no intrinsic value at the current underlying price. Exercising it immediately would generate no economic gain and, after transaction costs, would imply a loss, although the option may still be valuable because of the possibility that the underlying price moves favourably before expiry.^1,3,5,6,7

Formal definition and moneyness

The moneyness of an option describes the relationship between the option’s strike price and the current spot price of the underlying asset. An option can be:

• In the money (ITM) – positive intrinsic value.
• At the money (ATM) – spot price approximately equal to strike.
• Out of the money (OTM) – zero intrinsic value.^1,3,4,5,6

For a single underlying with spot price S and strike price K:

• A call option is OTM when S < K. Exercising would mean buying at K when the market lets you buy at S < K, so there is no gain.^1,3,4,5,6,7
• A put option is OTM when S > K. Exercising would mean selling at K when the market lets you sell at S > K, again implying no gain.^1,3,4,5,6,7

The intrinsic value of standard European options is defined as:

• Call intrinsic value: \max(S - K, 0).
• Put intrinsic value: \max(K - S, 0).

An option is therefore OTM exactly when its intrinsic value equals 0.^3,4,5,6

Intrinsic value vs time value

Even though an OTM option has no intrinsic value, it typically still has a positive premium. This premium is then made up entirely of time value (also called extrinsic value):^3,5,6

• Intrinsic value – immediate exercise value, which is 0 for an OTM option.
• Time value – value arising from the probability that the option might become ITM before expiry.

Thus for an OTM option, the option price C (for a call) or P (for a put) satisfies:

• C = \text{time value} when S < K.
• P = \text{time value} when S > K.⁶

Examples of out-of-the-money options

• OTM call: A stock trades at 30. A call option has strike 40. Buying via the option at 40 would be worse than buying directly at 30, so the call is OTM. Its intrinsic value is \max(30 - 40, 0) = 0.^2,3,4
• OTM put: The same stock trades at 30. A put has strike 20. Selling via the option at 20 would be worse than selling in the market at 30, so the put is OTM. Its intrinsic value is \max(20 - 30, 0) = 0.^3,4,5

OTM options at and after expiry

At expiry a standard listed option that is out of the money expires worthless. For the buyer this means:

• They lose the entire premium originally paid.^2,3,5

For the seller (writer):

• An OTM expiry is a favourable outcome – the option expires with no intrinsic value and the writer keeps the premium as profit.^2,5

Why OTM options still have value

Despite having no intrinsic value, OTM options are often actively traded because:

• They are cheaper than at-the-money or in-the-money options, so they provide high leverage to movements in the underlying.^2,3,5
• They embed a non-linear payoff that becomes valuable if the underlying makes a large move in the right direction before expiry.
• Their price reflects implied volatility, time to maturity and interest rates, all of which influence the probability of finishing in the money.

This makes OTM options attractive for speculative strategies seeking large percentage returns, as well as for hedging tail risks (for example, buying deep OTM puts as crash insurance). However, they have a higher probability of expiring worthless, so most OTM options do not end up being exercised.^2,3,5

OTM options in European option valuation

For European-style options – exercisable only at expiry – the value of an OTM option is purely the discounted expected payoff under a risk-neutral measure. In continuous-time models such as Black – Scholes – Merton, even a deeply OTM option has a strictly positive value whenever the time to expiry and volatility are non-zero, because there is always some probability, however small, that the option will finish in the money.

In the Black – Scholes – Merton model, the price of a European call option on a non-dividend-paying stock is

C = S\,N(d_1) - K e^{-rT} N(d_2)

and for a European put option

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

where N(\cdot) is the standard normal cumulative distribution, r is the risk-free rate, T is time to maturity, and d_1, d_2 depend on S, K, r, T and volatility \sigma. For OTM options, these formulas yield a positive price driven entirely by time value.

Strategic uses of OTM options

OTM options are integral to many derivatives strategies, for example:

• Speculative directional bets: Buying OTM calls to express a bullish view or OTM puts for a bearish view, targeting high percentage gains if the underlying moves sharply.
• Income strategies: Writing OTM calls (covered calls) to earn premium while capping upside beyond the strike; or writing OTM puts to potentially acquire the underlying at an effective discounted price if assigned.
• Hedging and risk management: Buying OTM puts as portfolio insurance against severe market declines, or constructing option spreads (for example, bull call spreads, bear put spreads) with OTM legs to shape payoff profiles cost-effectively.
• Volatility and tail-risk trades: OTM options are particularly sensitive to changes in implied volatility, making them useful in volatility trading and in expressing views on extreme events.

Key risks and considerations

• High probability of expiry worthless: Because the underlying must move sufficiently for the option to become ITM before or at expiry, many OTM options never pay off.^2,3,5
• Time decay (theta): As expiry approaches, the time value of an OTM option erodes, often rapidly, if the expected move does not materialise.
• Liquidity and bid-ask spreads: Deep OTM options can suffer from wider spreads and lower liquidity, increasing transaction costs.
• Leverage risk: Although the premium is small, the percentage loss can be 100 percent, and repeated speculative use without risk control can be hazardous.

Best related strategy theorists: Fischer Black, Myron Scholes and Robert C. Merton

The concept of an OTM option is fundamental to options pricing theory, and its modern analytical treatment is inseparable from the work of Fischer Black, Myron Scholes and Robert C. Merton, who together developed the Black – Scholes – Merton (BSM) model for pricing European options.

Fischer Black (1938 – 1995)

Fischer Black was an American economist and partner at Goldman Sachs. Trained originally in physics, he brought a quantitative, model-driven perspective to finance. In 1973 he co-authored the seminal paper “The Pricing of Options and Corporate Liabilities” with Myron Scholes, introducing the continuous-time model that now bears their names.

Black’s work is central to understanding OTM options because the BSM framework shows precisely how time to expiry, volatility and interest rates generate strictly positive values for options with zero intrinsic value. Within this model, the value of an OTM option is the discounted expected payoff under a lognormal distribution for the underlying asset price. The pricing formulas make clear that an OTM option’s value is highly sensitive to volatility and time – a key insight for both hedging and speculative use of OTM contracts.

Myron Scholes (b. 1941)

Myron Scholes is a Canadian-born American economist and Nobel laureate. After academic posts at institutions such as MIT and Stanford, he became widely known for his role in developing modern options pricing theory. Scholes shared the 1997 Nobel Prize in Economic Sciences with Robert Merton for their method of determining the value of derivatives.

Scholes’s contribution to the understanding of OTM options lies in demonstrating, together with Black, that one can construct a dynamically hedged portfolio of the underlying asset and a risk-free bond that replicates the option’s payoff. This replication argument gives rise to the risk-neutral valuation framework in which the fair value of even a deeply OTM option is derived from the probability-weighted payoffs under a no-arbitrage condition. Under this framework, the distinction between ITM, ATM and OTM options is naturally captured by their different sensitivities (“Greeks”) to underlying price and volatility.

Robert C. Merton (b. 1944)

Robert C. Merton, an American economist and Nobel laureate, independently developed a continuous-time model for pricing options and general contingent claims around the same time as Black and Scholes. His 1973 paper “Theory of Rational Option Pricing” extended and generalised the framework, placing it within a broader stochastic calculus and intertemporal asset pricing context.

Merton’s work deepened the theoretical foundations underlying OTM option valuation. He formalised the idea that options are contingent claims and showed how their value can be derived from the underlying asset’s dynamics and market conditions. For OTM options in particular, Merton’s extensions clarified how factors such as dividends, stochastic interest rates and more complex payoff structures affect the time value and hence the price, even when intrinsic value is zero.

Relationship between their theory and out-of-the-money options

Together, Black, Scholes and Merton transformed the treatment of OTM options from a qualitative notion – “currently unprofitable to exercise” – into a rigorously quantified object embedded in a complete market model. Their work explains:

• Why an OTM option commands a positive price despite zero intrinsic value.
• How that price should depend on volatility, time to expiry, interest rates and underlying price level.
• How traders can hedge OTM options dynamically using the underlying asset (delta hedging).
• How to compare and structure strategies involving multiple OTM options, such as spreads and strangles, using model-implied values and Greeks.

While many other theorists have extended option pricing and trading strategy – including researchers in stochastic volatility, jumps and behavioural finance – the work of Black, Scholes and Merton remains the core reference point for understanding, valuing and deploying out-of-the-money options in both academic theory and practical derivatives markets.