Option pricing formula is a mathematical formula used to calculate option price, among which the most famous formula is Black-Scholes option pricing model. This model was put forward by fischer black and Miron Skur in 1973 to calculate the European option price. Black-Scholes model assumes that:

The volatility of option price is constant;

The yield of option price is continuous, which accords with the random walk process;

Before the expiration date of the option, there is a certain correlation between the yield of the option price and the yield of the underlying asset.

The mathematical formula of Black-Scholes option pricing model is:

C = SN(d 1) - Ke(-rt)N(d2)

P = Ke(-rt)N(-d2) - SN(-d 1)

These include:

C stands for European call option price;

P stands for European put option price;

S represents the current price of the underlying asset;

K represents the exercise price of the option;

T represents the expiration time of the option;

R stands for risk-free interest rate;

D 1 and d2 are intermediate variables calculated according to the above assumptions, and the specific formula is:

d 1 =(ln(s/k)+(r+σ^2/2)t)/(σìt)

d2 = d 1 - σ√t

Where σ represents the volatility of the underlying assets and n represents the cumulative distribution function of the standard normal distribution.

Black-Scholes model is based on a series of assumptions and preconditions, and the actual situation may be biased. Therefore, when using this model for option pricing, it is necessary to make reasonable adjustments and corrections according to the actual situation.