NoteBook 1.4

[ArjunWhabi]

Hello

Firstly thanks so much for all your notebooks they are really helpful and insightful. Credit to you for all the effort.

However I noticed something in notebook 1.4

When you are generating rice paths using Hestons Model you use the following equation :

for t in range(0,N-1):
    v = np.exp(Y[:,t])    # variance 
    v_sq = np.sqrt(v)     # square root of variance 
    
    Y[:,t+1] = Y[:,t] + (1/v)*( kappa*(theta - v) - 0.5*sigma**2 )*dt + sigma * (1/v_sq) * dt_sq * W_v[:,t]   

    X[:,t+1] = X[:,t] + (mu - 0.5*v)*dt + v_sq * dt_sq * W_S[:,t]

However, According to Euler Method shoulndt it be as follows: for i in range(1,N+1): S[i] = S[i-1] * np.exp( (mu- 0.5*v[i-1])*dt + np.sqrt(v[i-1] * dt) * Z[i-1,:,0] ) v[i] = np.maximum(v[i-1] + kappa*(theta-v[i-1])*dt + sigma*np.sqrt(v[i-1]*dt)*Z[i-1,:,1],0) I could be wrong but just thought id check

[cantaro86]

Hi @ArjunWhabi , both approaches are correct. I used Euler Maruyama (EU) discretization on the system of two SDEs, you instead used the EU method only on the variance SDE. You used the analytical solution for the price.