Question

Homework 4 Due April 27, 2020 On February 1st, September call option with exercise price of $55 written on Aztec stock is sold for $4.375 per share and September put option with exercise price of $55 written on the same stock is sold for $6 per share. At the time, T-bills coming due in September are priced to yield 12%. Aztec stock is sold for $53 per share on February 1st. The time period between Feb 1 st and expiration date of options is 8 months. 1. If the call option, Aztec stock, and T-bills are correctly priced, what is the appropriate value of a put option on February 1st? (1 point) 2. How to take advantage of this situation? Please show arbitrage profits using arbitrage table. (2 points)

Answer 1

Put Call Parity

Put-call parity states that a fiduciary call should be equal to protective put. Fiduciary call means buying a call and investing in the PV of the strike price which ensures we have cash to buy the asset. Protective put is a position where we buy a put and we also buy a stock so that it limits the downside of a stock.

i.e Call + PV (Strike Price) = Put + Stock

Value of Fiduciary call = 4.375 + PV (55)

We need to discount 55 by 8 months @12% pa

= 4.375 + 55 / (1+12%*8/12)

= 4.375 + 50.9259

=55.3009

Value of Protective Put = Put + Stock

= 6 + 53 = 59

As fiduciary call is not equal to protective put, arbitrage opportunity exists:

Step 1: Buy fiduciary call and sell protective put

Buy call and Invest 50.9259 , hence total outflow 55.3009

Sell put and sell stock , hence total inflow 59

Net Inflow is 3.6991

Step 2: Close the position

Value of options includes 2 components - Time value and Intrinsic Value. At expiration only intrinsic value will be there as there wont be any time value.

Value of Call at expiration = Stock Price (S)- Strike Price (X) (Where S> X) or 0 (Where X < equal to S)

Value of Put at expiration = Strike Price (X) - Stock Price (S) (Where X < S) or 0 (Where S>equal to X)

We will sell the call now, hence any value to call will be an inflow

We will buy the put now, hence any value to put will be an outflow

We will redeem investment which will be inflow and we will buy stock which will be outflow

Stock Price	50	55	60
Sell Call	0	0	5
Redeem Investment	55	55	55
Buy Put	-5	0	0
Buy Stock	-50	-55	-60
Net	0	0	0

Hence whatever may be the price, there wont be any additional outflow and we have made a risk free profit of 3.6691 on 'day 0' of investment.