The price of a European call that expires in six months and has a strike price of $49 is $4.5. The underlying stock price is $50, and a dividend of $1.00 is expected in three months. The term structure is flat, with all risk-free interest rates being 10%.
a. What is the price of a European put option that expires in six months and has a strike price of $49? [1 mark]
b. Explain in detail the arbitrage opportunities if the European put price is $1.60. How much will be the arbitrage profit? [4 marks]
Put call parity with known dividend : C + PV (Strike Price) = S - PV (Dividend) + P
where C is the price of call option, P is the price of Put option and S is the current stock price.
PV strike price = 49 * e-10%*0.5 = 46.61
PV dividend = 1 * e-10%*0.25 = 0.98
Plugging in the values we get:
4.5 + 46.61 = 50 - 0.98 + P ; or P = 2.09
b. However if the Put price is 1.60, then the RHS of the put call parity will be less than the LHS side of the equation. Hence a trader can profit by arbitraging as below:
The price of a European call that expires in six months and has a strike price...
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