Question

Question 4

Suppose European call and put options on St Barbara Ltd are selling for $0.35 and $0.24, respectively. Both options are struck at $4.85 and mature in nine months. The current stock price of St Barbara Ltd is $3.84 and the risk-free rate is 3.2% p.a. Is there an arbitrage opportunity in this market? Indicate what strategy you would implement in taking advantage of any arbitrage opportunity and the profit you would earn from your strategy (Note: You are required to outline the initial and terminal values of your strategy).

Answer 1

Step 1: Identifying arbitrage opportunity exist or not.

As per put-call parity theory, Call premium+Present value of strike price = Put premium+Current stock price. If the above put-call parity theory holds good, there is no arbitrage opportunity exist, else there is a chance for arbitrage opportunity.

Given in question, call premium = $0.35; put premium = $0.24; current stock price = $3.84; Strike price = $4.85; risk free rate (rf) = 3.2% p.a; time (t) = 9 months

Present value of strike price = strike price*[e^(-trf)] = $4.85*[2.718^(-0.032*9/12)] = $4.85*[2.718^-0.024] = $4.85*(0.9763) = $4.735

Put call theory, $0.35+$4.735 = $0.24+$3.84

$5.085 = $4.08, Since the equation does not hold good, Arbitrage opportunity exist.

Step 2: Strategy identification

In put-call parity equation, left hand side is over valued, hence short sell & right side is undervalued buy it now. Sell the call option, buy the share & put option, Strategy is "Write the call, hold the put & buy the share"

Step 3: Determination of arbitrage profit

Action	Amount
Write call option & receive premium	-$0.35
Buy put option & pay	$0.24
Buy the share	$3.84
Initial Net outflow	$3.73

Borrow the initial net outflow of $3.73 for 9months @ 3.2%

Maturity amount = Borrowing amount*[e^(trf)] = $3.73*[2.718^(0.032*9/12)] = $3.73*[2.718^0.024] = $3.73*(1.0243) = $3.8222

On maturity date (After nine months)

Action	Actual price < $4.84	Actual price = $4.84	Actual price > $4.84
Call option	Holder allow the call to lapse	Holder allow the call to lapse	Holder exercise the call
Put option	Exercise the put	Allow the put to lapse	Allow the put to lapse
Stock status	Give the stock to writer of put option @ $4.84	Sell in open market @ $4.84	Give the stock to holder of call option @ 4.84
Profit after repaying borrowings ($4.84-$3.8222)	$1.0178	$1.0178	$1.0178

Arbitrage profit per unit = $1.0178