Question

Value of a stock is currently at $40. Volatility of that stock is 30% per year and risk-free interest rate with continuous compounding is at 5% per year. Suppose you are planning to value a 3-month European call option with strike price at $41 using a two-step binomial model. Answer the following using this information. (Binomial Tree Approach to Option Valuation describe how to solve this problem)

What are the values of u, d and q?

Answer 1

uret dre ovi = 1

u = e^(0.3*(3/12)^(1/2)) = 1.1618

d = 1/u = 1/1.1618 = 0.8607

Step 5 Binomial Tree Pricing Step 1 Step 2 Scenario price-Spot price*(U)^2=40*1.1618^2=53.99 Payoff HH=Max(Scenario price-Strike price,0) =Max(53.9911696-41,0) =Max(12.9911696,0) =12.9911696 Call option value at node H=e^(-r*t)*(*Payoff HH+(1-9)Payoff HL) =e^(-0.05-0.25)*(0.504412 12.9911696+(1-0.504412)*0) =6.4715 Risk neutral probability for up move q=(e^(risk free rate time)-D)/(U-D) =(e^(0.05*0.25)-0.8607)/(1.1618-0.8607)=0.50441 Node HE =Max(5.47199999999999,6.4715)=6.4715 Node H Step 3 Scenario price=Spot price*(U)*(D)=40*1.1618*0.8607=40 Payoff HL=Max(Scenario price-Strike price,0) =Max(39.9984504-41,0) Node HL =Max(-1.0015496,0) =0 T=0 Today T=0.25 T=0.5 Nodel Step 6 Step 7 Call price = e^(-r*t)*(q*Node H value+(1-9)Node L value) =e^(-0.05-0.25)*(0.504412*6.4715+(1-0.504412)*0) -3.2238 Call option value at node L= e^(-r*t)*(q*Payoff HL+(1-9)*Payoff LL) =e^(-0.05-0.25)*(0.504412*0+(1-0.504412)*0) Step 4 Node LL Scenario price=Spot price*(U)^2=40*0.8607^2=29.63 Payoff LL=Max(Scenario price-Strike price, 0) =Max(29.6321796-41,0) =Max(-11.3678204,0) 20 =Max(0,0)=0