Question

Suppose that the stock price is $31, the risk-free interest rate is 9% per year, the price of a three-month European call option is $2.70, and the price of a 3-month European put option is $2.24. Both options have the strike price $29. Assume monthly compounding. Describe an arbitrage strategy and justify it with appropriate calculations. Please write your solution in complete sentences.

Answer 1

	As per Put Call Parity Theorem,
	S+P = C+PV of E
	Where,
	Risk Free Rate = 9%
	Risk Free Rate for 3 months = r = 9%*3/12 = 2.25% = 0.0225
	S = Stock Price = $31
	P = Value of Put Option = $2.24
	C = Value of Call Option = $2.70
	PV of E = Present Value Exercise Price
	= Strike Price / (1+r)
	= $29 / (1+0.0225)
	= $29 / (1.0225)
	= $28.36
	Now,
	S+P = C+PV of E
	$31 + $2.24 ǂ $2.70 + $28.36
	$33.24 ǂ $31.06
	As here is violation of Put Call Parity Theorem, arbitrage
	opportunity exists.
	Here, Stock Price and Put is overpriced and Call and Risk Free
	Investments are underpriced, so arbitrage opportunity will involve -
	1. Buy Call Option and Risk Free Investment
	2. Short sell Share and Put Option
	Arbitrage Gain will be
	Sale of Share			31.00
	Sale of Put			2.24
	Buy a Call Option			(2.70)
	Buy a Risk Free Investment (PV of E)	(28.36)
					2.18
	So, Arbitrage gain will be $2.18.