The Black-Scholes model, also known as the Black-Scholes-Merton (BSM) model, is one of the most important concepts in modern financial theory. It provides a mathematical formula that calculates the theoretical value of derivatives based on investment vehicles, taking into account the effect of time and other risk factors.
From the parabolic partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price given the risk of the security and its expected return (instead replacing the security’s expected return with the risk-neutral rate).
The Black-Scholes model requires five input variables: the strike price of an option, the current stock price, the time to expiration, the risk-free rate, and the volatility.
- C = call option price
- S = current stock price
- K = strike price
- r = risk free interest rate
- t = time to maturity
- N = normal distribution
With these variables, it is theoretically possible for options sellers to set reasonable prices for the options they sell.
When was the Black-Scholes model developed?
The Black-Sholes model has been in development since 1973. It is still the best method for pricing options contracts.
How Accurate Is Black-Scholes Pricing?
Although it is usually accurate, the Black-Scholl model makes certain assumptions that may cause prices to deviate from real market results.
Why not use the Black-Scholes model in pricing US options?
The standard BSM Black-Scholes model is used only for pricing European options. This is because it does not take into account the possibility of exercising US options before the expiration date.
What are the assumptions of the Black-Scholes model?
The Black-Scholes model is based on several assumptions: no dividends are paid during the life of the option, and there are no transaction costs when purchasing the option. Also, the returns of the underlying assets are distributed normally. And prices move in random markets (market movements cannot be predicted). On the other hand, the risk-free rate and volatility of the underlying assets are known and stable. Finally, the option can only be exercised upon expiration.
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