Black-Scholes Option Pricing
Calculate theoretical option prices using the Black-Scholes-Merton model.
What is this tool?
The Black-Scholes-Merton model is the foundational mathematical framework for pricing European-style options. It calculates theoretical option prices based on five inputs: underlying price, strike price, time to expiration, risk-free interest rate, and volatility. The model assumes constant volatility and log-normal price distribution. Despite its limitations, it remains the industry standard for quick option valuation.
How to use
- 1
Enter underlying price
Type the current price of the underlying asset.
- 2
Set strike and expiry
Enter the option strike price and days until expiration.
- 3
Configure volatility and rate
Input the annual volatility percentage and risk-free rate.
- 4
View pricing results
See theoretical call and put prices, d1/d2 values, intrinsic value, time value, and ITM/OTM status.
Frequently Asked Questions
What is the Black-Scholes model?
The Black-Scholes model is a mathematical formula developed in 1973 that calculates theoretical option prices. It revolutionized financial markets and earned its creators the Nobel Prize. The formula gives closed-form solutions for European options and is the basis for most professional option pricing systems.
What are the model's limitations?
Key assumptions include constant volatility (unrealistic), no dividends (simplified), log-normal price distribution (fat tails exist), and continuous trading (markets close). It cannot price American-style early exercise. For these reasons, practitioners use extensions like Merton dividend model, stochastic volatility models (Heston), and binomial trees.
What do d1 and d2 represent?
d1 relates to the probability that the option will be in-the-money at expiration. d2 is d1 minus the volatility-adjusted distance, representing the risk-neutral probability of exercise. N(d1) is used in the delta calculation, while N(d2) gives the probability that the option expires ITM.