Question

1. The current price of stock XYZ is $100. Stock pays dividends at the continuously compounded yield rate of 4%. The continuously compounded risk-free rate is 5% annually. In one year, the stock price may be 115 or 90. The expected continuously compounded rate of return on the stock is 10%. Consider a 105-strike 1-year European call option. Find the continuously compounded expected rate of discount γ for the call option.

Answer 1

solution Given that, Current Share price = So - $100 Stock price in case of up movement (su)= $115 stock price in case of down movement (si) = $90 Risk free rate vp = 5% . Expected Continciously compounded rate ' of return = f(2)=10% Compound dividend yield qz4% strike price of call = $105 up movement of dock price Us Su Downmovement of stock price D= Sai $100 -70.90 probability of upmovement of stock price The = eer-cult -ol CSScanned with cascanner U-D

Tu : where a risk free rate e dividend yield. (56-47.Jxt -090 115-0.90 -0.44e44% Time of maturity of call t= 1 year. Td = probability of down movement of stock price Td a 1-Tlu 31–44% - $-0.44 -10.56 1 e 15674 pay off in case of a Man CS-x,0) European Call When share price is 115 le Su = $115, then pay off of european call = man (115-105,0) $10 When share price is 90 ie d = $90 then by off of european Call-man (90-105,0) man (-15,0) price of European Call = $10 xTu totd aften ly with = = 10844% strike = 105 $414] i price of European Call = $4.4.. CS Scanned with CamScanner

is present value of European call with strike = $105 is $404 = 4.4 5701 i continuonly Compounded expected -1$ 4:1854] rate of return y for the call option risk free rate 25% - The End - CSScanned with CamScanner