Question

urrently, the stock price is $50. Over each of the next two 1-yr periods it is expected to go up by 20% or down by 20%. The risk-free rate is 5% per annum with continuous compounding.

What is the value of a 2-yr European call option with a strike price of $61? Round to the nearest cent. For example, if your answer is $12.345, then enter 12.35. Margin of error: +/- 0.10.

Answer 1

Step 5 Binomial Tree Pricing Step 1 Step 2 Scenario price-Spot price*(U)^2=50*1.2^2=72 Payoff HH=Max(Scenario price-Strike price,o) =Max(72-61,0) =Max(11,0) =11 Call option value at node H=e^(-r*t)*(q*Payoff HH+(1-9)*Payoff HL) Fe^(-0.05*1)*(0.628178*11+(1-0.628178)*o) =6.573 Risk neutral probability for up move q = (enfrisk free rate*time)-D)/(U-D) =(e^(0.05*1)-0.8)/(1.2-0.8)=0.62818 Node HH =Max(0,6.573)=6.573 Node H Step 3 Scenario price=Spot price*(U)*(D)=50*1.2*0.8=48 Payoff HL=Max(Scenario price-Strike price,0) =Max(48-61,0) =Max(-13,0) T=0 Today T=1 T=2 Node HL Node L Step 6 Step 7 Call price = e^(-r*t)*(q*Node H value+(1-9)*Node Lvalue) =e^(-0.05*1)*(0.628178*6.573+(1-0.628178)*o) =3.9276 Call option value at node L=e^(-r*t)*(q*Payoff HL+(1-9)*Payoff LL) =e^(-0.05*1)*(0.628178*0+(1-0.628178)*0) Step 4 Node LL Scenario price=Spot price*(U)^2=50*0.8^2=32 Payoff LL-Max(Scenario price-Strike price,0) =Max(32-61,0) =Max(-29,0) -Max(0,0)=0

therefore value of call option = 3.93