# Options Pricing – A Guide for Traders and Investors

Options pricing is often considered to be complex and confusing. Many investors and traders shy away from options due to their perceived difficulty in understanding and calculating. So, in this post, we will clearly understand what is options pricing and break down the key concepts and formulas that govern this method of trading.

## What is Option Pricing?

Option pricing refers to the process of valuing an options contract. This financial derivative gives the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price within a specified period.

It plays a crucial role in determining the fair value of an options contract, providing investors with insights into the potential profitability and risk associated with options trading.

The significance of option pricing lies in its ability to estimate the fair value of an options contract based on various factors, such as the current price of the underlying asset, the strike price, the time to expiration, and market volatility.

By using option pricing models, such as the Black-Scholes or the binomial model, traders and investors can calculate the expected value of an option and make informed decisions regarding buying or selling options.

Accurate option pricing is essential for both buyers and sellers of options. It helps buyers assess the potential return on investment and decide whether the cost of the option is justified. On the other hand, sellers can use option pricing to determine the appropriate premium to charge for assuming the risk associated with the options contract.

## Option Pricing Models

In finance, these models are tools used to determine the fair value of options contracts. They provide a framework for estimating the value of an option based on several key factors.

One commonly used pricing model is the Black-Scholes model, which considers variables such as the current price of the underlying asset, the strike price, time to expiration, risk-free interest rate, and market volatility.

This model assumes that the underlying asset follows a geometric Brownian motion and provides a mathematical formula for pricing European-style options. Another widely used model is the binomial model, which divides the time to expiration into discrete intervals and calculates the probability of the stock price moving up or down at each interval.

This model allows investors to determine the value of American and European-style options. Additionally, Monte Carlo simulations model option prices by simulating numerous random paths for the underlying asset’s price and averaging the results.

These models offer different methodologies for option valuation and provide investors with valuable insights when making decisions in the options market.

## Black-Scholes Formula

The Black-Scholes formula is a widely recognised mathematical model used for pricing options. Developed by economists Fischer Black and Myron Scholes in 1973, this formula revolutionised the field of options pricing.

The Black-Scholes formula considers several key components to determine the fair value of an option. These components include the current price of the underlying asset, the strike price of the option, the time to expiration, the risk-free interest rate, and the market volatility.

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The formula assumes that the underlying asset follows a geometric Brownian motion, meaning that its price changes are random and follow a continuous distribution.

The formula goes as follows:

C = S*N(d1) – Ke^(-rt)*N(d2)

Where:

• C = Price of call option

• S = Current stock price

• K = Strike price

• r = Risk-free interest rate

• t = Time to maturity

• e = Exponential term

• N(d) = Cumulative normal distribution

And:

d1 = (ln(S/K) + (r + σ^2/2)t) / (σ√t) d2 = d1 – σ√t

σ = Volatility of the underlying asset

The key inputs are:

• The current stock price.

• The option’s strike price.

• The risk-free rate.

• The time to maturity.

• The volatility.

The formula uses the normal distribution to calculate the probability that the option will expire in the money. It then calculates the present value of the expected payoff.

## Intrinsic Value

Intrinsic value is a key concept in options pricing that represents the profit that could be realised if the option were to be exercised immediately.

It is defined as the difference between the current price of the underlying asset and the strike price of the option. For call options , if the underlying asset’s current price is higher than the strike price, the option has a positive intrinsic value.

This means that exercising the option would result in an immediate profit equal to the difference between the asset and strike prices. On the other hand, for put options, if the underlying asset’s current price is lower than the strike price, the option has a positive intrinsic value.

In this case, exercising the option allows the holder to sell the asset at a higher price than its current market value, resulting in an immediate profit.

Understanding intrinsic value is crucial in option pricing models as it provides insight into the potential profit that can be captured by exercising an option.

## Formula and Calculation of Intrinsic Value

To calculate the intrinsic value of an option, specific formulas depend on whether it is a call or a put option. For call options, the formula to compute the intrinsic value is as follows:

Intrinsic Value (Call) = Current Price of Underlying Asset – Strike Price

This formula calculates the difference between the current market price of the underlying asset and the strike price of the call option. If the result is positive, it indicates that the option has intrinsic value.

Similarly, for put options, the formula is slightly different:

Intrinsic Value (Put) = Strike Price – Current Price of Underlying Asset

In this case, the calculation subtracts the current market price of the underlying asset from the strike price. If the result is positive, it signifies that the put option holds intrinsic value.

## Example of Intrinsic Value

Let’s consider a real-world example for a company called ABC Ltd. Suppose you are analysing a call option for ABC Ltd with a strike price of Rs 500. The current market price of the ABC Ltd stock is Rs 600. Using the formula for call options, the intrinsic value would be:

Intrinsic Value (Call) = ₹600 – ₹500 = ₹100

In this case, the option has an intrinsic value of Rs 100 because the current stock price is Rs 100 above the strike price. This means if you were to exercise the call option now, you would gain Rs 100 per share.

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So, for an Indian stock option, the intrinsic value is calculated the same way – by taking the difference between the current market price of the underlying stock and the strike price stated in the option contract.

## Time Value

Time value represents the additional value attributed to an option due to the time remaining until its expiration. Time value is determined by factors such as the length of the option’s remaining lifespan, the volatility of the underlying asset, and prevailing interest rates.

As time passes, the potential for the option to move in-the-money or out-of-the-money changes. This uncertainty causes option prices to fluctuate. The longer the time until expiration, the greater the potential for the underlying asset’s price to change, increasing the likelihood of the option becoming profitable. So, options with more time remaining until expiration tend to have a higher time value.

## Formula and Calculation of Time Value

The formula for calculating the time value of an option is straightforward. It can be derived by subtracting the option’s intrinsic value from its total market price.

The intrinsic value is determined by comparing the strike price of the option with the current price of the underlying asset. The intrinsic value will be positive if the option is in-the-money (favourable strike price). On the other hand, if the option is out-of-the-money (the strike price is not favourable), the intrinsic value will be zero.

To compute the time value, subtract the intrinsic value from the total option price. This time value represents the premium associated with the option’s time remaining until expiration. It encapsulates the uncertainty and potential for future price movements.

The formula for calculating the time value is as follows:

Time Value = Option Price – Intrinsic Value

## Example of Time Value

Let’s consider a real-life example to better understand the time value calculation for an option in the Indian market. Suppose an investor purchases a call option on a stock with a strike price of Rs 100. The stock’s current market price is Rs 110.

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In this case, the option’s intrinsic value would be Rs 10 (Rs 110 – Rs 100). However, the total market price of the option is Rs 15.

To calculate the time value, we subtract the intrinsic value from the total option price: Rs 15 – Rs 10 = Rs 5. This Rs 5 represents the time value, reflecting the potential for the option to gain further value as the expiration date approaches.

## Conclusion

Investors can make more informed decisions when buying or selling options by considering the various factors that influence an option’s price, such as the underlying stock’s price, implied volatility, and time until expiration. As with any investment, it is important to carefully research and consider all risks before making any trading decisions.