Question

Given: C = $4.75, P = $3.25, S = $42, K = $40, T = 6 months, r = 2% p.a.

a.    What would you do to exploit these quotes? (List the transactions.) What would be your riskless arbitrage profit?

b.    How could you synthetically short-sell an asset using only options and borrowing or lending at the risk-free rate? Would you be better off short-selling the stock, or synthetically short-selling it using options?

Answer 1

a)
According to put call parity:
C+X/(e^rt)=S+P
4.75+40/e^0.02*0.5=42+3.25
44.35 is not equal to 45.25

To have arbitrage gains, sell the higher valued side and buy lower valued side
Hence sell protective put side and buy covered call side
Short sell stock and sell a put. Buy a call option. (45.25-4.75)=40.50
Invest the proceed in risk free rate.
After six months:
Cancel out share with call option at 40
Get back invested sum = 40.50*e^0.01=$40.91
Arbitrage gain = $0.91