Question

A three-month call option on a stock is currently selling at $5. The current stock price is $65, the strike price for the option is $60. The risk - free rate is 10% p.a. for all maturities.

a.) Is there any opportunity for an arbitrageur? Explain

b.) Show the strategy how an arbitrageur can obtain the arbitrage profit. What will the profit be? Show workings

Answer 1

Arbitrage opportunity is an opportunity to earn profit without making any investment and taking any risk. This opportunity normally arise when asset is not fairly priced or not in equilibrium.

a).

To check whether arbitrage opportunity exist or not in above case, we need to first calculate the Fair price of 3-month call option. we can use following equation to calculate the Call fair price-

Where,

S = Current Stock Price

E = Exercise price

r = risk free rate

t = maturity time

Given:

S = $65

E = $60

r = 10%

t = 3/12 = 0.25

putting the values -

Fair value of Call option > Actual Call Price

Thus, Arbitrage opportunity exist.

b.)

Strategy to earn arbitrage profit :

1. Short sell Stock at current price $65

2. Buy Call option at $5 with Strike Price $60

3. Deposit $60 i.e remaining balance of short sale proceed after paying call premium at risk free rate .

On Maturity -

If Stock Price > $60

Deposit proceed on maturity = 60*e^0.025 = 61.51891

Exercise the call option and buy stock at $60

Net Profit from arbitrage = 61.51891 - 60 = $1.51891

If Stock Price < $60

Do not exercise the call option and buy stock at low price from deposit proceed and keep the difference as arbitrage profit.

Hope this will help, please do comment if you need any further explanation. Your Feedback would be appreciated.