Question

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

Answer 1

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