Trinomial Pricer.py

import numpy as np
import math

### Parameters ###

sigma = 0.3
T = 200
dt = 1/2000

q = 0.  #dividendes rate
r = 0.5 #free-risk rate
S0 = 20

u = math.exp(sigma * math.sqrt(2*dt))
d = 1/u
m = 1


pu = ((math.exp((r-q) * dt/2) - math.exp(-sigma * math.sqrt(dt/2))) / 
     (math.exp(sigma * math.sqrt(dt/2)) - math.exp(-sigma * math.sqrt(dt/2))))**2

pd = ((math.exp(sigma * math.sqrt(dt/2)) - math.exp((r-q) * dt/2)) /
     (math.exp(sigma * math.sqrt(dt/2)) - math.exp(-sigma * math.sqrt(dt/2))))**2

pm = 1 - pu - pd

#Formulas taken from wikipedia, see : https://www.wikiwand.com/en/Trinomial_tree#/Formula

### init_price() est une fonction qui sert à déterminer la valeur de l'actif sous-jacent S, à chaque noeud de l'arbre ###

def init_price(N):    
    STs = [np.array([S0])]

    for i in range(N):
        prev_nodes = STs[-1] #At each loop, take the last element of the list
        ST = np.concatenate((prev_nodes*u, [prev_nodes[-1]*m, prev_nodes[-1]*d]))
        STs.append(ST)
    return STs
    
### payoff_compute() sert à déterminer le prix de l'option, à chaque noeud de l'arbre ###
    
def payoff_compute(STs,N, K) :
    
    callMatrix = [None] * N #Empty list of size N
    putMatrix  = [None] * N #Empty list of size N
    
    for i in reversed(range(N)):        
        if(i == N-1) :            
            payoffCall = np.maximum(0, max(STs[i]-K))  #The payoff list is sorted, so take the first one
            payoffPut  = np.maximum(0, max((K-STs[i])))#The payoff list is sorted, so take the first one
        else :            
            payoffCall = math.exp(-(r-q)*dt) * (pu*callMatrix[i+1] + pd*callMatrix[i+1] + pm*callMatrix[i+1])
            payoffPut  = math.exp(-(r-q)*dt) * (pu*putMatrix[i+1] + pd*putMatrix[i+1] + pm*putMatrix[i+1])
        
        callMatrix.insert(i,payoffCall)
        putMatrix.insert(i,payoffPut)
    return callMatrix, putMatrix    
    
    
STs = init_price(20)
c,t = payoff_computer(STs,20, 18)

print("Avec le model trinomial, le prix du put devrait etre", t[0])
print("Avec le model trinomial, le prix du put devrait etre", c[0])