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You observe that the stock XYZ is currently trading at $8
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?
Expert Solution
A) Condition which is violated here of Black-Scholes is that $0.25 dividend is due in a month's time, this assumption is false because no dividend is paid in the life of option according to Black-Scholes model.
B) To calculate benefit due to violation we need:
Intrinsic value of option = Stock price - Strike price (Given)
= $8.5 - $8.00
= $0.5
Price of put and call option is $0.45 and $0.65 respectively.(Given)
So, arbitrage process should be done with call option because put option is lower than intrinsic amount and buyer will have to pay premium higher than intrinsic value.
C) To calculate arbitrage profit we need:
Current trading price (A) = $8.50 (Given)
Selling price of call option with strike price (B) = $8.00 (Given)
Premium (C) = $0.65 (Given)
Now, formula to calculate arbitrage profit is = (B + C - A)
= ($8.00 + $0.65 - $8.50)
= $0.15
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