Question

On November 1, 20-n, you notice the following bid-ask quotes in the option market (supposedly perfect otherwise!), the underlying asset being stock ABC:

Call 130 January: 11-12

Call 145 January: 7-8

Put 130 January: 8.5-9.5

Put 145 January: 16-17

ABC quotes 133 and the 3-month interest rate is 4% (proportional, annualized rate).

a) What arbitrage should you undertake (transaction costs are negligible, but you are not market-maker, so that you are subject to the bid-ask spread)?

b) Is it really riskless?

c) What is its IRR if you do not cancel, either by lending or by borrowing, the initial cash-inflow or outflow?

Answer 1

Every option has two prices at any time of the trading day. The first price is called the "bid" or sell price, and it's the price at which you could sell the option. ... The second price is the "ask" or buy price. That is the price at which you can buy an option.

Recall the Call Put Parity Equation:

C - P = S - PV (K)

K = strike Price = 130

LHS = C - P = Buy a call + Short (Sell) a Put = 12 - 8.5 = 3.5

RHS = S - PV (K) = 133 - 130 x (1 + 4% x 3 / 12)^-1 = 4.29

RHS = S - PV(K) > LHS = C - P

Hence, S - PV(K) + P - C > 0

Part (a)

Hence, the arbitrage strategy should be:

• Borrow Present value of the strike price
• Short sell the call
• Buy the stock
• Buy the put option

Part (b)

Yes, it is really riskless.

Part (c)

IRR = Riskless return = 4%