Homework #3 for MAFS 5220

""" author: Stan Wang; assignment 3 : trinomial tree for option pricing; """ import networkx as nx import numpy as np def tri_option_grid(S,dt,u,d,pu,pd,pm,numsim): G = nx.Graph() G.add_node((0,0),value=S,time=0) for i in range(0,numsim): for j in range(0,2*i+1): currentvalue = G.node[(i,j)]['value'] G.add_node((i+1,j),value=currentvalue*u,time=(i+1)*dt) G.add_node((i+1,j+1),value=currentvalue,time=(i+1)*dt) G.add_node((i+1,j+2),value=currentvalue*d,time=(i+1)*dt) G.add_edge((i,j),(i+1,j),value = pu) G.add_edge((i,j),(i+1,j+1),value = 1-pu-pd) G.add_edge((i,j),(i+1,j+2),value = pd) return G # the class for simple call and put class simpleCall: def __init__(self,strike,maturity): self.strike = strike self.maturity = maturity def payoff(self,price): return max(price - self.strike, 0) class simplePut: def __init__(self,strike,maturity): self.strike = strike self.maturity = maturity def payoff(self,price): return max(self.strike - price, 0) def option(strike,maturity,c_p): if c_p==0: return simpleCall(strike,maturity) else: return simplePut(strike,maturity) # set the terminal payoff for option def set_terminal_payoff(G,n,derivative): for i in range(0,2*n+1): G.node[(n,i)]['option'] = derivative.payoff(G.node[(n,i)]['value']) #backward def backward_induction(G,n,discount,derivative,e_a): for i in range(n-1,-1,-1): for j in range(0,2*i+1): nextup = G.node[(i+1,j)]['option'] nextm = G.node[(i+1,j+1)]['option'] nextdown = G.node[(i+1,j+2)]['option'] nextupprob = G[(i,j)][(i+1,j)]['value'] nextmprob =G[(i,j)][(i+1,j+1)]['value'] nextdownprob =G[(i,j)][(i+1,j+2)]['value'] undis = nextup*nextupprob+nextm*nextmprob+nextdown*nextdownprob G.node[(i,j)]['option'] = max(undis * discount,e_a*derivative.payoff(G.node[i,j]['value'])) return G.node[(0,0)]['option'] def tri_option_price(S # stock price ,K # strike price ,T # maturity ,numsim # number of simulations ,sigma # vol ,r # riskless rate ,e_a # 0 means European option, 1 means Amercian option ,c_p # 0 means Call option, 1 means Put option ): dt = T/float(numsim) u = np.exp(sigma * np.sqrt(2*dt)) d = 1/u numerator = np.exp(sigma*np.sqrt(dt/2))-np.exp(-sigma*np.sqrt(dt/2)) pu = ((np.exp(r*dt/2)-np.exp(-sigma*np.sqrt(dt/2)))/numerator)**2 pd = ((np.exp(sigma*np.sqrt(dt/2))-np.exp(r*dt/2))/numerator)**2 pm = 1-pu-pd stepdiscount = np.exp(-r * dt) derivative = option(K,T,c_p) G = tri_option_grid(S,dt,u,d,pu,pd,pm,numsim) set_terminal_payoff(G,numsim,derivative) option_price = backward_induction(G,numsim,stepdiscount,derivative,e_a) return option_price print(tri_option_price(100,100,1,255,0.1,0.05,0,0))