Option Pricing Using Binomial Trees

10 Questions
Option Pricing Using Binomial Trees
Sample Question

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:

6.1 cents

5.7 cents

5.3 cents

4.9 cents

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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