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A stock price has an expected return of 16% and a volatility of 25%. The current price is $38. What is the prices of European call and put options (Using The Black-Scholes-Merton Model) on the stock with an exercise price of $40 and a maturity date in six-months? Assume that risk free interest rate is 6%.

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Deanna Hettinger
Deanna HettingerLv2
28 Sep 2019

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Suppose you hold LLL employee stock options representing options to buy 10,400 shares of LLL stock. LLL accountants estimated the value of these options using the Black-Scholes-Merton formula and the following assumptions:

S = current stock price = $24.67

K = option strike price = $25

r = risk-free interest rate = .042

σ = stock volatility = .32

T = time to expiration = 3.5 years

You wish to hedge your position by buying put options with three-month expirations and a $30 strike price. How many put option contracts are required?

1)The current price of a stock is $100. What is the Black-Scholes model price of a six-month call option at strike $101, given an interest rate of 2% and a dividend rate of 1%? The volatility is 25%.
(a) $6.30
(b) $6.52
(c) $6.56
(d) $6.78

2)The current price of a stock is $100. What is the Black-Scholes model price of a six-month put option at strike $98, given an interest rate of 2% and a dividend rate of 1%? The volatility is 45%.
(a) $11.02
(b) $11.22
(c) $11.68
(d) $11.73

The following information is given about options on the stock of a certain company.

Current stock price = $114
Exercise price = $115
Continuously compounded risk-free rate = 0.1 percent Time to expiration = 6 months (T = 0.5) in June
The volatility = 0.28

(1) Find the values of N(d1) and N(d2)

(2) What value does the Black-Scholes-Merton model predict for the call?

(3) What is the delta of the call?

(4) If the stock price goes up by $1 to $115, what would be the call price based on the delta?

(5) Suppose that June 115 call has the gamma of .0176. If the stock price goes up by $1 to $115, what would be the delta of the call based on the gamma?

(6) Suppose that the call rho (ρ) is 25.523. If the continuously compounded risk-free rate goes up by 1 percent to 1.1 percent, what would be the expected call price based on the rho?

(7) Suppose that the call vega (ν) is 32.106. If the volatility of the continuously return on the stock increase by 1 percent, what would be the expected call price based on the vega?

(8) Suppose that the theta (θ) is 9.04. If the time to expiration decreases so that the call expires in 3 months (T = .25), what would be the expected call price based on the theta?

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