Option Pricing Using Binomial Trees
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- 1.Using the Black Scholes formula, calculate the price of a 4-month European call option on the British pound. You are given the following details: The current exchange rate is 1.3, the exercise price is 1.3. The risk free interest rate in the United States is 3% per annum whereas the risk free rate in Britain is 4% per annum. The annualized implied volatility in the exchange rate is 20%. The European call option price is:
- A.
6.1 cents
- B.
5.7 cents
- C.
5.3 cents
- D.
4.9 cents
- 2.What are the values of u, d and p when a binomial tree is constructed to value an option on a foreign currency. The tree step size is 1 month, the domestic interest rate is 5% per annum, the foreign interest rate is 8% per annum, and the volatility is 12% per annum.
- A.
1.035, 0.966, 0.455
- B.
1.035, 0.966, 0.527
- C.
1.039, 0.963, 0.451
- D.
1.039, 0.963, 0.530
- 3.Use the conventional binomial tree method with n=3 steps to calculate the price of a 4-month American put option on the British pound. You are given the following details: The current exchange rate is 1.3, the exercise price is 1.3. The risk free interest rate in the United States is 3% per annum whereas the risk free rate 4% per annum. The annualized implied volatility in the exchange rate is 10%. The price of the American put option is:
- A.
2.7 cents
- B.
2.9 cents
- C.
3.2 cents
- D.
3.4 cents
- 4.Recalculate the price of the American put option given in question 3 above using n=30 steps. Hint: use Mark Broadie’s efficient Binomial tree method. What is the price of the option:
- A.
3.1 cents
- B.
3.2 cents
- C.
3.3 cents
- D.
3.4 cents
- 5.The difference between the value of an European Call option calculated by the Black-Scholes formula and that calculated using Binomial trees arises because the Binomial Tree method uses a discrete number of times steps where Black Scholes assumes continuous hedging and rebalancing of the portfolio.
- A.
True
- B.
False
- 6.For an American option the value of the option at a node other than the terminal node is:
- A.
The expected present value of option at successor nodes
- B.
The payoff from early exercise
- C.
The minimum of the expected present value of option values at successor nodes or the payoff from early exercise
- D.
The maximum of the expected present value of option values at successor nodes or the payoff from early exercise
- E.
None of the above
- 7.For a European up-and-out call option the option will only be exercisable and exercised at expiry if:
- A.
The barrier is reached during the tenor of the option and the spot price on maturity is less than the strike price
- B.
The barrier is reached during the tenor of the option and the spot price on maturity exceeds the strike price
- C.
The barrier is not reached during the tenor of the option and the spot price on maturity exceeds the strike price
- D.
The barrier is not reached during the tenor of the option and the spot price on maturity is less than the strike price
- E.
None of the above
- 8.The accuracy of calculating the value of a American call option using the binomial tree method can always be improved by increasing the number of time steps used in the calculation.
- A.
True
- B.
False
- 9.The accuracy of calculating the value of a down and out call option using the binomial tree method can always be improved by increasing the number of time steps used in the calculation.
- A.
True
- B.
False
- 10.The sensitivity of an option’s price to volatility of the underlying’s price is measured by the following Greek:
- A.
Delta
- B.
Gamma
- C.
Rho
- D.
Theta
- E.
Vega
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