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).
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
Question 4 Suppose European call and put options on St Barbara Ltd are selling for $0.35...