tion4(total of 8 marks): Consider a one year American call option with a strike

Question

tion4(total of 8 marks): Consider a one year American call option with a strike price of a dividend paying stock currently trading at $10. The dividend is paid annually and the next expected to be $1, paid in 6 months. The risk-free interest rate is 5% standard deviation of the stock's retums is 20% pa. $9, written on dividend is p.a. continuously compounded and the the option price now (t-0) using either the no-arbirage approach or the risk-neutral approach with a two-step binomial tree with 6 months per step. Remember that the option is American so it can be exercised before maturity. There are formulas on the formula sheet to help. You may wish to use the binomial tree below to work out the answer

Explanation / Answer

Calculation of Call option Price using General Method:(No Arbitage Approach) Option Price: Spot price-Pv of Strike Price Spot Price 10 Strike Price 9 Risk Free Rate (Compounded Continuously) (e^0.05) 5%                                                                                             (e=2.71828) So; 10 - (1/(2.71828^0.05)) 1.44 Calculation of Call option Price using Risk Neutral Method: Probability of High Price= (R-D)/(U-D) R; Risk Free Rate: e^5% U; 1+%upward Movement in Price=20% D; 1-%Downward Movement In Price=20% e^(0.025)-(1-0.2) / (1+0.2)-(1-0.2) As 6 period binominal tree is given so 5% rate is equalized for 6months i.e 2.5% P(High Price)=Approx :        56.33% P(Low Price)=(1-56.33%)= 43.67%    Calculation of Payoff At 1 Yr end MP SP Action Payoff Probability Expected Payoff (MP-SP) 15.633(Expected High Price At 6 mths end)Node B NODE D 24.44(15.633+56.33%) 9 Exercise 15.44 56.33%                                        8.70 NODE E 8.81(15.633-43.67%) 9 Lapse(As sp

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