Option price calculation methods

Valuation of options

Option pricing theory uses variables stock price, exercise price, volatility, interest rate, time to expiration to theoretically value an option.

Intrinsic value[ edit ] The intrinsic value is the difference between the underlying spot price and the strike price, to the extent that this is in favor of the option holder. For a call optionthe option is in-the-money if the underlying spot price is higher than the strike price; then the intrinsic value is the underlying price minus the strike price. For a put optionthe option is in-the-money if the strike price is higher than the underlying spot price; then the intrinsic value is the strike price minus the underlying spot price. Otherwise the intrinsic value is zero. This is called the time value.

Essentially, it provides an estimation of an option's fair value which traders incorporate into their strategies to maximize profits. Some commonly used models to value options are Black-Scholesbinomial option pricingand Monte-Carlo simulation. Understanding Option Pricing Theory The primary goal of option pricing theory is to calculate the probability that an option will be exercised, or be in-the-money ITMat expiration.

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Underlying asset price stock priceexercise pricevolatilityinterest rateand time to expiration, which is the number of days between the calculation date and the option's exercise date, are commonly used variables that are input into mathematical models to derive an option's theoretical fair value.

Aside from a company's stock and strike prices, time, volatility, and interest rates are also quite integral in accurately pricing an option.

As a result, time value is often referred to as an option's extrinsic value since time value is the amount by which the price of an option exceeds the intrinsic value. Time value is essentially the risk premium the option seller requires to provide the option buyer the right to buy or sell the stock up to the date the option expires. Typically, stocks with high volatility have a higher probability for the option to be profitable or in-the-money by expiry. As a result, the time value—as a component of the option's premium—is typically higher to compensate for the increased chance that the stock's price could move beyond the strike price and expire in-the-money.

The longer that an investor has to exercise the option, the greater the likelihood that it will be ITM at expiration. Similarly, the more volatile the underlying asset, the greater the odds that it will expire ITM.

Since the underlying random process is the same, for enough price paths, the value of a european option here should be the same as under Black Scholes. More generally though, simulation is employed for path dependent exotic derivativessuch as Asian options.

Higher interest rates should translate into higher option prices. Real traded options prices are determined in the open market and, as with all assets, the value can differ from a theoretical value.

However, having the theoretical value allows traders to assess the likelihood of profiting from trading those options. The evolution of the modern-day options market is attributed to the pricing model published by Fischer Black and Myron Scholes.

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The Black-Scholes formula is used to derive a theoretical price for financial instruments with option price calculation methods known expiration date. However, this is not the only model.

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The Cox, Ross, and Rubinstein binomial options pricing model and Monte-Carlo simulation are also widely used. Key Takeaways Option pricing theory uses variables stock price, exercise price, volatility, interest rate, time to expiration to theoretically value an option. The primary goal of option pricing theory is to calculate the probability that an option will be exercised, or be in-the-money ITMat expiration.

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Some commonly used models to value options are Black-Scholes, binomial option pricing, and Monte-Carlo simulation. Also, implied volatility is not the same as historical or realized volatility. Currently, dividends are often option price calculation methods as a sixth input.

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Additionally, the Black-Scholes model assumes stock prices follow a log-normal distribution because asset prices cannot be negative. Other assumptions made by the model are that there are no transaction costs or taxes, that the risk-free interest rate is constant for all maturitiesthat short selling of securities with use of proceeds is permitted, and that there are no arbitrage opportunities without risk.

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Clearly, some of these assumptions do not hold true all of the time. For example, the model also assumes volatility remains constant over the option's lifespan.

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This is unrealistic, and normally not the case, because volatility fluctuates with the level of supply and demand. However, for practical purposes, this is one of the most highly regarded pricing models.

FRM: Binomial (one step) for option price

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