The price of a European call that expires in 3 months and has a strike price of

Question

The price of a European call that expires in 3 months and has a strike price of $30 is $3. The underlying stock price is $31. The stock pays no dividends. Risk-free interest rate is 10% per annum with continuous compounding. A. Suppose that the price of a European put with the same maturity and strike price is $1. Describe the arbitrage opportunity and compute the arbitrage profit. B. Now suppose that the stock pays a dividend of $0.50 in 2 months. Find the price of the European put (with 3-month maturity and strike price of $30 (typo corrected)) using the put-call parity with dividends.

Explanation / Answer

1)

Put call parity

C + X*EXP(-r*T) = P + S

P = C + X*EXP(-r*T) - S

Call (C) = 3, Strike X = 30, Stock S = 31, r = 10%

P = 3 + 30*EXP(-0.1*0.25) - 31 = 1.26

Using put call parity Put should be priced at 1.26, so there is an arbitrage existed

Buy the put, Buy the stock, and short the call => 1+31-3 = 29 , in 3 months it will be = 29*EXP(-0.1*0.25) = 29.73

Whatever the stock price, either put or call would be in the money and will be exercised at 30.

The short call and long put option position would therefore leads to the stock being sold for 30. Hence, the net profit generated by the arbitrageur is

30-29.73 = 0.27

2)

P = C + X*EXP(-r*T) - D*EXP(-r*T1) + S

T1 = 2/12 , D = 0.5

P = 3 + 30*EXP(-0.1*0.25) - 0.5*EXP(-0.1*0.25) - 31 = 0.77

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.