# Optional Pricing : What Is Optional Theory?

September 30, 2021
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Optional Pricing : Option pricing theory calculates the value of an options contract by allocating a premium based on the calculated chance that the contract will expire in the money (ITM).

Option pricing theory, in essence, gives a calculation of an option’s fair value, which traders use in their tactics.

## What Is Option Pricing Theory and How Does It Work?

To theoretically value an option, models used to price options account for variables such as current market price, strike price, volatility, interest rate, and time to expiration.

Black-Scholes, binomial option pricing, and Monte-Carlo simulation are some of the most often used models for valuing options.

### Keypoints to remember:

Option pricing theory is a probabilistic technique to determining an option’s value.

Option pricing theory’s main purpose is to figure out how likely an option will be exercised, or in the money (ITM), at expiration.

If the maturity or implied volatility of an option is increased while all other factors remain constant, the option’s price will rise.

The Black-Scholes model, binomial tree, and Monte-Carlo simulation method are some of the most often used models for pricing options.

## Option Pricing Theory: An Overview

Option pricing theory’s main purpose is to determine the likelihood that an option will be exercised, or be in the money, at expiration and assign a cash value to it.

The underlying asset price (for example, a stock price), exercise price, volatility, interest rate, and time to expiry, which is the number of days between the calculation date and the option’s exercise date, are all common variables used to calculate an option’s notional fair value.

Based on those inputs, options pricing theory produces various risk factors or sensitivities, which are referred to as an option’s “Greeks.”

The Greeks give traders a way to determine how sensitive a trade is to price variations, volatility swings, and the passage of time, because market circumstances are continuously changing.

The greater the likelihood that the option will expire in the money and be profitable, the higher the option’s value, and vice versa.

The longer an investor has to execute an option, the more likely it is to be ITM and profitable when it expires.

Longer-dated options are therefore more valued, assuming all other factors are equal.

Similarly, the more volatile the underlying asset, the more likely it is to expire in the money. Higher interest rates should result in higher option pricing as well.

### Particular Points to Consider

Non-marketable options and marketable options require distinct valuation approaches.

The value of real traded options is determined on the open market, and it can differ from a theoretical value, as it does with other assets.

Having the theoretical value, on the other hand, allows traders to gauge their chances of gaining from trading those options.

Fischer Black and Myron Scholes’ 1973 pricing model is credited with laying the groundwork for today’s options market.

For financial instruments with a known expiration date, the Black-Scholes formula is used to calculate a theoretical price.

This isn’t the only model, though. The binomial option pricing model of Cox, Ross, and Rubinstein, as well as Monte-Carlo simulation, are also commonly employed.

### The Black-Scholes Option Pricing Theory is used

The strike price of an option, the current price of the stock, the time to expiration, the risk-free rate of return, and volatility were the five input variables in the original Black-Scholes model.

Because it is hard to predict future volatility directly, it must be estimated or inferred.

As a result, implied volatility differs from historical or realised volatility.

Dividends are frequently used as a sixth input for various stock options.

Because asset prices cannot be negative, the Black-Scholes model, one of the most widely used pricing models, assumes stock prices follow a log-normal distribution.

The model also assumes that there are no transaction fees or taxes, that the risk-free interest rate is constant across all maturities, that short selling of assets with proceeds is allowed, and that there are no risk-free arbitrage opportunities.

Clearly, several of these assumptions are incorrect all of the time, if not the majority of the time.

The model, for example, assumes that volatility remains constant throughout the option’s lifetime.

This is ridiculous, and it isn’t usually the case, because volatility varies with supply and demand.

Volatility skew, which refers to the form of implied volatilities for options graphed across a variety of strike prices for options with the same expiration date, will be included in option pricing model changes.

The implied volatility values for options further out of the money (OTM) are higher than those at the strike price closer to the price of the underlying instrument, resulting in a skew or “smile.”

Furthermore, Black-Scholes presupposes that the options being valued are European-style options that can only be exercised at maturity.

The model does not account for the exercise of American-style options, which can be exercised at any moment up to and including the day before they expire.

The binomial or trinomial models, on the other hand, can handle both types of options since they can check for the option’s value at any point during its life.