Question

a) (13 pts) A stock price is currently $49. It is known that at the end of 6 months it will be either $57 or $42. The risk-free rate of interest with continuous compounding is 11% per year. Calculate the value of a 6-month European call option on the stock with an exercise price of $48 using both the no-arbitrage arguments and risk-neutral valuation arguments. Show that they provide the same answers. 9. (25 pts) Please write the solution for this problem on paper. Use statistical table attached at the end of the exam. Do not use Excel.

b) (12 pts) Consider an option on a non-dividend-paying stock when the stock price is $42, the exercise price is $41, the annual risk-free interest rate is 2.5%, the volatility is 20% per annum, and the time to maturity is a quarter. (a) What is the price of the option according to the Black-Scholes-Merton formula if it is a European call? (b) What is the price of the option if it is an American call? (c) What is the price of the option if it is a European put?

Answer 1

B)

a)

Here

S = 42

X=41

rf= 0.025

Standard deviation = 0.2

time T= 3 months or 3/12 = 0.25

d1 = LN(42/41)+((0.025+0.2/2)*0.25)/(0.2*SQRT(0.25)) = 0.55

d2 = 0.55-(0.2*SQRT(0.25)) = 0.45

Value of N(d1) and N(d2) can be find out through below table.

Call Value=

42*NORMSDIST(0.55)-41*NORMSDIST(0.45)*EXP(-0.025*0.25)=2.32

b) the value of American Call will be same approx.

c) value of european put

P =

2.32+41*EXP(-0.025*0.25)-42

=1.064 approx.

thanks

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