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Find the premium of a correctly priced interest rate call on 30-day LIBOR if the current forward rate is 7 percent, the strike is 7 percent, the continuously compounded risk-free rate is 6.2 percent, the volatility is 12 percent and the option expires in one year. The notional amount is $30 million

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Elin Hessel
Elin HesselLv2
30 Sep 2019

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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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A stock index currently stands at 300 and has a volatility of 20% per year. The continuously compounded risk-free interest rate is 3% per year and the dividend yield on the index is 8%. Use a TWO-STEP binomial tree to value a six-month American call option on the index with a strike price of 295. Show all calculations.

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