Homework #3 for MAFS 5220

"""author: Stan Wang;assignment 3 : trinomial tree for option pricing;"""import networkx as nximport numpy as npdef 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 putclass 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 optiondef 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'])#backwarddef 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_priceprint(tri_option_price(100,100,1,255,0.1,0.05,0,0))