An alternative to using Black and Scholes model is using Constant Elasticity of Variance model.
This is a diffusion model where the risk neutral process for a stock is
dS=(r-s)*S*dt - sigma*S^alpha*dZ
Input:
S- underlying price.
K- strike price
r- risk free rate
T- time to maturity
sigma- std of the underlying asset
q- yield to maturity of the underlying asset
alpha- Elasticity of variance
Outputs:
call- the price of call option
put- the price of put option
Example:
[call,put]=constantElasticity(50,50,0.04,1,0.3,0,1)
Reference:
[1] Options,Futures and other Derivatives, seventh edition by John Hull |