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
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
call- the price of call option
put- the price of put option
 Options,Futures and other Derivatives, seventh edition by John Hull
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