# Option Pricing Using Binomial Trees

10 Questions  Settings  Questions and Answers
• 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

Related Topics