have an account?【sign in】Implied Volatility Price Formula: Understanding the Implied Volatility Price in Options Trading
bannaauthorImplied volatility, also known as the implied volatility price, is a crucial concept in options trading. It represents the expected volatility of the underlying asset for a given time horizon, and it is calculated using the Black–Scholes–Merton (BSM) formula. Understanding the implied volatility price is crucial for successful options trading, as it helps traders make informed decisions about their positions and risk management. In this article, we will explore the implied volatility price formula and how it can be used in options trading.
The Black–Scholes–Merton Formula
The Black–Scholes–Merton formula is a mathematical model that was developed in the 1970s to calculate the price of a European call option when the underlying asset has a standard normal distribution. The formula takes into account the following factors:
1. S: The current stock price of the underlying asset
2. X: The number of days until expiration of the option
3. K: The current strike price of the option
4. r: The annual risk-free rate of return
5. σ: The annual implied volatility of the asset
Calculating the Implied Volatility Price
To calculate the implied volatility price, we first need to find the current implied volatility, which can be done using a volatility swap or by using the BSM formula. Once the implied volatility is known, it can be used to calculate the option price.
Let's assume we have the current stock price (S), the expiration date (X), the strike price (K), and the current implied volatility (σ). We can use the BSM formula to calculate the option price, P, as follows:
P = SN(d1) - K×e^(-r×X)×SN(d2)
where N(d1) and N(d2) are the normal cumulative distribution functions of the standard normal distribution, and d1 and d2 are related to the implied volatility as follows:
d1 = (X/σ) - (√(X²/σ²) - X)
d2 = (X/σ) + (√(X²/σ²) - X)
Inversing the Implied Volatility Price
Sometimes, it is more useful to know the implied volatility in terms of the option price instead of the stock price. In this case, we can invert the BSM formula to find the implied volatility in terms of the option price, as follows:
σ = (P×√(2/X))÷e^(X/2)
Understanding the implied volatility price formula and how to calculate it is crucial for successful options trading. The implied volatility price provides valuable insights into the expected volatility of the underlying asset and can be used to make informed decisions about position sizing, risk management, and trading strategies. As the options market continues to grow and become more complex, having a strong understanding of the implied volatility price will become increasingly important for successful trading.