Question

You observe that the stock XYZ is currently trading at $8.50. The continuously compounded volatility is 20% p.a. The stock is due to pay a $0.25 dividend going ex-dividend in 1 month’s time. 3-month European call and put options written on XYZ trading at $0.65 and $0.45 respectively. The strike price on both options is $8.00. The continuously compounded risk free rate is 6%pa.

a) Which theoretical Black-Scholes condition is violated?

b) Clearly describe the arbitrage process you would perform to take advantage of the violation.

c) What is your arbitrage profit?

Answer 1

a) One of the Assumptions underlying the Black and Scholes Model is that the stock pays no dividends during the Option's life.However it is specified in the Question that Stock is due to pay $ 0.25 Dividend in 1 month's time.Therefore, this assumption is violated.

b) Given Stock XYZ is trading at $ 8.5 and Strike Price is $ 8.Therefore,intrinsic value of the option = STOCK PRICE - STRIKE PRICE = $ 8.5- $ 8.00 = $ 0.5 and Price of call and put options is $ 0.65 and $ 0.45 respectively.

As Put Option is less than intrinsic value of option it is better to do arbitrage process with Call Option

The Buyer of call option will have to pay premium which is more than intrinsic value of the option i.e 0.65-0.50 = 0.15 Loss.

Therefore it is better to be a writer of call option.

A writer of call option will do the following actions

Buy a Stock in Spot Market at (A) $ 8.50

Sell a Call Option with Strike Price at (B) $ 8.00

Receive Premium (C) $ 0.65

Arbitrage Profit (B+C-A) $ 0.15