Shout options

A shout option is a standard European option except that the option buyer can shout to the option seller before maturity date to set the minimum payoff as Sτ-X, where Sτ is the stock price at time τ when the buyer shouts and X is the exercise price. The level of the strike could be set at a specific relation to the spot price, such as 3% or 5% above (or below). The Python codes are given here:

def shoutCall(s,x,T,r,sigma,shout,n=100):
    from math import exp,sqrt
    import numpy as np
    deltaT = T /n
    u = exp(sigma * sqrt(deltaT)) 
    d = 1.0 / u
    a = exp(r * deltaT)
    p = (a - d) / (u - d)
    v =[[0.0 for j in np.arange(i + 1)] for i in np.arange(n + 1)] 
    for j in np.arange(n+1):
        v[n][j] = max(s * u**j * d**(n - j) - x, 0.0) 
    for i in np.arange(n-1, -1, -1):
        for j in np.arange(i + 1):
            v1=exp(-r*deltaT)*(p*v[i+1][j+1]+(1.0-p)*v[i+1][j]) 
            v2=max(v[i][j]-shout,0)   # shout  
            v[i][j]=max...