Question

# A European call option on a stock with a strike price of \$75 and expiring in...

A European call option on a stock with a strike price of \$75 and expiring in six months is trading at \$5. A European put option on the stock with the same strike price and expiration as the call option is trading at \$15. The current stock price is \$64 and a \$2 dividend is expected in three months. Zero coupon risk‐free bonds with face value of \$100 and maturing after 3 months and 6 months are trading at \$99 and \$98, respectively. Identify the arbitrage opportunity open to a trader.

PLEASE SHOW ALL WORK AND EXPLANATIONS

Put call parity condition = C0+(D+X*e-r*t) = P0+ S0

Interest rate for 3 month

Face value/Price = (1+r)t

100/99 = (1+r)3/12

1.01 = (1+r)3/12

1.03 = 1+r

r = 0.03 or 3 %

Interest rate for 6 month

Face value/Price = (1+r)t

100/98 = (1+r)612

1.02 = (1+r)6/12

1.04 = 1+r

r = 0.04 or 4 %

Present value of dividend = 2e-rt

= 2e-0.03*3/12

= 2e-0.0075

= 2/1.00753

= 1.98

Put call parity condition

5 + 1.98+75e-0.04*6/12 = 15 + 64

80.50 < 79

Trader should buy put option and stock and short call option and bond

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