Question

Spot price	50
Strike price	50
Effective annual risk-free rate	1%
Continuous Dividend Yield	0
Time to maturity	1 year
European Call Option Premium	5.2
u	1.2
d	0.8

(a) Suppose you observe a call price of $5.50. How can you arbitrage?

A. Long call, long stock and borrow money.

B. Short call, long stock and borrow money.

C. Long call, short stock and lend money.

D. Short call, short stock and lend money.

(b) What is the present value of the arbitrage profit?

Answer 1

50 50 196 ice Strike Effective annual risk-free rate Continuous Dividend Yield Time to maturi 1 year 5.2 1.2 0.8 European Call Option Premium Risk Nuetral probabilty of UP move-(1+1%-0.8)/(1.2 0.8)- 0.525 Risk Nuetral Probabilty of Down move 1-0.525 0.475 60 50*1.2-Stock Price for up move 10 -MAX(0,60-50) Call Option Value 50 40 50*0.8-Stock Price for Down move 0-MAX(0,40-50) Call Option Value Expected Value of Call Option in 1 Year (10*0.525)+(0*0.475) 5.25 Value of the option Today 5.25/(1+0.01) 5.198019802 Since the value of the Call option is trading higher in the Market caompared to the value calculated above, therefore in order to profit from Arbitrage we should Short cal, long stock and borrow money Arbitrage Profit Calculation Delta - 0.5 Proceed From Short Call - Buy of Stock 50*0.5 5.5 25 19.50 Net Portfolio Cost 25-5.5 Value of the Portfolio at Maturity in Up Move (0.5 60)-(10) Value of the Portfolio at Maturity in Down Move(0.5 40)-(0) 20.00 20.00 Portfolio Retun = 20-19.5 0.50 Interest on Loan =19.5*(1.01)-19.5 0.195 0.31 0.30198 Arbitrage Profit-0.5-0.195 Present value of Arbitrage 0.305/(1+1%)