Question

Compute the European put price using a two-period binomial model. S0 = 10, T = 2 months, u = 1.5, d = 0.5, r = 0.05, K = 7, D=0.

Answer 1

We are required to prepare following two-period binomial model

Given data:

Stock price (S0) = 10

T = 2 months

Up move factor (U) = 1.5

Down move factor (D)= .5

Risk free rate (r) = 0.05

Strike price (K) = 7

Now, Risk neutral probability up move P_u = ((1+r) – D)/ (U-D)

                                                            = ((1+0.05)-0.5)/(1.5-0.5)

                                                            = 55%

Risk neutral probability down move    P_D = 100-P_U

                                                            = 45%

Stock Price (X at t= 0) = S0 = 10

Stock Price (X_U at t= 1) = X*U = 10*1.5 = 15

Stock Price (X_D at t= 1) = X*D = 10*0.5 = 5

Stock Price (X_UU at t= 2) = X_U*U = 15*1.5 =22.5

Stock Price (X_UD at t= 2) = X_U*D = 15*0.5 =7.5

Stock Price (X_DU at t= 2) = X_D*U = 5*1.5 =7.5

Stock Price (X_DD at t= 2) = X_D*D = 5*0.5 =2.5

Option Payoff (at t=2) = P_upup = Max [(X_UU - X),0] = 15.5

Option Payoff (at t=2) = P_updn = P_dnup   = Max [(X_UD - X),0] = 0.5

Option Payoff (at t=2) = P_dndn = Max [(X_DD - X),0] = 0.0

Option Payoff (at t=1) = P_up = [(P_upup * P_u ) + (P_updn * P_D)] / (1+r) = 8.33

Option Payoff (at t=1) = P_dn = [(P_updn * P_u ) + (P_downdn * P_D)] / (1+r) = 0.26

Option Payoff (at t=0) = c = [(P_up * P_u ) + (P_dn * P_D)] / (1+r) = 0.26 = 4.48

Putting these values in the above two-period binomial model