Enter the stock price, strike price, expiry date, and volatility into the calculator to determine your option price.

Options Pricing Formula

The following formula is used to calculate the option price. 

Option Price = S * N(d1) - X * e^(-rT) * N(d2)

Variables:

  • Option Price is the price of the option ($)
  • S is the stock price ($)
  • X is the strike price ($)
  • r is the risk-free interest rate (%)
  • T is the time to expiry (years)
  • N(d1) and N(d2) are the cumulative distribution functions of the standard normal distribution.

To calculate the option price, multiply the stock price by N(d1), subtract the strike price multiplied by e to the power of -rT and N(d2).

What is Options Pricing?

Options pricing refers to the process of determining the fair value of an options contract. This involves understanding the factors that influence the option’s price, such as the underlying stock price, strike price, time to expiry, volatility, and risk-free interest rate. Accurate options pricing is crucial for making informed investment decisions and managing risk effectively.

How to Calculate Option Price?

The following steps outline how to calculate the option price using the given formula.

  1. First, determine the stock price, strike price, time to expiry, volatility, and risk-free interest rate.
  2. Next, calculate d1 and d2 using the Black-Scholes formula.
  3. Use the formula from above: Option Price = S * N(d1) – X * e^(-rT) * N(d2).
  4. Finally, calculate the option price by plugging in the values.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Stock Price = $150

Strike Price = $160

Expiry Date = 1 year from today

Volatility = 20%

Interest Rate = 5%

FAQ

1. What is the Black-Scholes model?

The Black-Scholes model is a mathematical model used for pricing options. It helps in calculating the theoretical value of options using factors like stock price, strike price, time to expiry, volatility, and risk-free interest rate.

2. How does volatility affect option pricing?

Volatility reflects the uncertainty or risk associated with the underlying asset’s price. Higher volatility increases the option’s price as it implies a higher probability of significant price movements.

3. Why is the risk-free interest rate important in options pricing?

The risk-free interest rate is used to discount the strike price to its present value. It represents the time value of money and impacts the option’s price calculation.

4. Can this calculator be used for American options?

This calculator is designed for European options, which can only be exercised at expiry. American options, which can be exercised anytime before expiry, require a different pricing model.

5. Is the calculator accurate?

The calculator provides an estimate of your option price based on the Black-Scholes model. For exact figures, it’s best to consult with a financial advisor or use professional financial software.