Question

. The spot price per share is $115 and the risk free rate is 5% per annum on a continuously compounded basis. The annual volatility is 20% and the stock does not pay any dividend. All options have a one-year maturity. In answering the questions below use a binomial tree with three steps. Each step should be one-third of a year. Show your work.

1.Using the binomial tree, compute the price at time 0 of a one-year European call option on 100 shares of stock with a strike price of $115 per share and show that put-call parity holds.

Answer 1

DATE Given, Spo Price of Share -$115 Risk Free Rate=r S% -0.0S t= time IYesr Strike Price -$11S Annual Volotilty - 20% Share Price at the end of Tear Spot Rice t 20% (i-e-Annual Volailiy $115+20% $11S-20% $138 -$92 Option Value at the end of Year Emax Share Price at the end of Year) Strite Price), o Max92-11s),0 Max C13s-11),0 max [-23, 0 23, 0 $23 Now Colcula ton of Option Delta Difference in Option Vahes Option Del ta (A)- Diference n Shaot Prices $23-0 $138-$92

$ 23 $ 4C O So Calculation O/ Porifolio Volue on where portfolio Consists of 1o0 Shares 4 &Coll oplion Expiry Date Share Prices $138 $92 Value of Shares l0oshares x $/38x Ae oS $6900 $4600 100 Shares x$92xAe.o.S EVolue of Cal /00x $23 ($2300) $44600 $4600 Calalaion of Rresent Vaue of Portfolio Present Valuue of Portfolio Porttoio Vahue on Expiry Dete et $ 14 600 (2.7183).0SX) $4600 (2.71 83) 0S $4 600 -$4p380.95

DATE Colulation OL Present Value of Call Option Present value of Share (-) Present Vake of Call Ophan Preseni Value of Porttolio $ 11S X A-) PU ot Coll Option4380 9S $11SX0.SX)00 (-) RUof Cal) Option 4380 9S PV of Call Option S7SO()4380-5 -$1369-0S