Question

Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. Use the Black-Scholes-Merton formula.

1. What is the price of the option if it is a European call?
2. What is the price of the option if it is an American call?
3. What is the price of the option if it is a European put?
4. Verify that put–call parity holds.

Answer 1

page toi Answer Given details. Stock price =$30 exercise pouce = 429 risk free interest rate = 5»l(per annum) Volality =25(per annum) .. time to maturity = 4 months. By using Black - Scholes a menton formula we howe to calculate the following below a) price of the option if it is a curopean call in this case So =30, k=24,7= 0.05, a 20-25 and t = 4112 in( 30/29)+10.05 +0.25^ (2) x 4112 at 0.0510.3333 - inciso din 0.0339015+ 0.08125 x 0.333 0.1443303 0.060982105 01443303 - 0,42295

pagetoa de, in(30129) + (0.05-0.251/2) x4412 0.25 10.3333 0 , 033 015 + 0, 0 815 x 0. 233 0.1443303 0,04014525 0.1443303 = 0,2782 N( 0.4225) = 0, 66 31, N( 0 2482) =0.606 N (-0.4225) 2 0.3363, N (0.2482) = 6,3904 The european call police is 30 X 0.6637 - 29-0,05% 4/12 X0.6096 30 X 0.6634 - 99 .983471 0.6096 19.911 - 28.520 659 x0.6096 -19.94 - 17.38619373 = 2.524 Therefore letopean call price is 2,52 (0) $19.527 b) průce of the option if it is an american call The american call price is the same as the european coil price it is (4 0.52

c) price of the option if it is a european put page :03 -0,05 * 4112 =) 290-01 X 0.3904 - 30X O. 3363 » 29x0.983471 X 0.3904 - 10.089 - 28.520659 X0,3904-10.089 - 11.1344652-4-10-089 1.045 31.05 Therefore Curopean put price 1.015 (89) 141.051 d) Verify that put -call parity holds. P+S=C ke- in this case C=2.52, So = 30, K-29, P=.05 and e t = 0.9835 and it is easy to verify that the relationship is satisfied

Answer 2

The present value of the dividend must be subtracted from the stock price.