have an account?【sign in】black-scholes implied volatility formula excel:An Introduction to Black-Scholes Implied Volatility Formula in Excel
cranfordauthorBlack-Scholes Implied Volatility Formula in Excel: An Introduction
The Black-Scholes implied volatility formula is a popular tool used in derivatives pricing and risk management. It is based on the work of Robert Merton and Myron Scholes, who developed the formula in the 1970s. The formula allows traders and investors to calculate the implied volatility of a stock or index option using the current price of the option and the underlying asset. In this article, we will explore the Black-Scholes implied volatility formula and how to use it in Excel.
The Black-Scholes Formula
The Black-Scholes implied volatility formula is based on the following assumptions:
1. The asset follows a normal distribution, also known as a Gaussian distribution.
2. The asset's price does not change over the life of the option.
3. The time to expiration of the option is known.
4. The implied volatility is a constant over the life of the option.
The formula for implied volatility is:
IV = sqrt(2 * (r - q) / (N(d1) - N(d2)))
Where:
IV - Implied volatility
r - Risk-free rate
q - Stock price volatility
N(x) - Standard normal cumulative distribution function
d1 and d2 - Normal probability distribution functions
Calculating Implied Volatility in Excel
To calculate implied volatility in Excel, follow these steps:
1. Enter the current stock price (S), risk-free rate (r), and stock price volatility (q) in cells A1, B1, and C1, respectively.
2. Enter the option's expiration date in cell A2.
3. Enter the option's strike price in cell B2.
4. Enter the option's time to expiration in days in cell C2.
5. Enter the formula in cell D2, as follows:
=SQRT(2*((B1-C2)/C2)^2)/(N(NDE(RAND()))-N(NDE(RAND()))+1)
6. Press Ctrl + Shift + Enter to calculate the implied volatility. The result will be in cell D2.
Example
Suppose the current stock price is $50, the risk-free rate is 3%, the stock price volatility is 20%, and the option's expiration date is one year away. The strike price is $50, and the time to expiration is one year.
In this case, the implied volatility would be calculated as follows:
1. Enter the specified values in cells A1, B1, C1, A2, and B2.
2. Enter the specified values in cells C3 and D3.
3. Press Ctrl + Shift + Enter to calculate the implied volatility. The result will be in cell D3.
In this example, the implied volatility would be approximately 12.5%.
The Black-Scholes implied volatility formula is a powerful tool for calculating the implied volatility of options and other derivatives. By using this formula in Excel, traders and investors can better understand the volatility of their investments and make more informed decisions. While the assumptions of the formula may not always be accurate, it remains a valuable tool for pricing options and managing risk.