More Practice for Final


K Foster, Options & Futures, Eco 275, CCNY, Spring 2010



Note: Exam will be in computer lab NAC 6150. You should plan to save all of your work and submit it via Blackboard.


More practice problems:


  1. Bond valuations – find continuous & discrete time answers:

    1. A strip bond pays its face (100) in 12 months. Current value is 95.5997. What is 12-month zero rate?

    2. A strip bond pays face (100) in 18 months; current value is 91.7365. What is 18-month zero rate?

    3. Three bonds from same issuer pay semiannually. Bond A expires in 18 months, pays 6.25% coupon semiannually, price is 103.96. One has 5.25% coupon and matures in one year; price is 102.05. Other has 6.5% coupon and matures in 6 months; price is 101.71. What are the 3 zero rates? The forward rates?

  2. Show payoffs for following portfolios of derivatives; stock has current price of 100:

    1. put with strike of 102; put with strike of 99; call with strike of 95

    2. strangle at 96, 99 plus share of stock

    3. put with ATM strike and share of stock

    4. butterfly spread of calls with strikes of 95, 98, 99

  3. Assume gold price is 100 and can go up to 105 or down to 98 over next 4 months; riskfree rate is 2%. Use tree to find:

    1. call price with strike of 99

    2. put price with strike of 99

    3. Use Black-Scholes-Merton formula to find option prices (what is reasonable value for volatility, given asymmetric tree – maybe use a range?)

  4. Assume soybeans are at 50 and can go up to 60 or down to 40 in next 12 months; riskfree rate is 3.5%. Use tree to find:

    1. values of ATM call & put,

    2. value of bull spread with strikes of 99 and 101

    3. Use Bl-S-M to find values.

  5. Use Black-Scholes-Merton formula to find option prices, delta, gamma, and VaR for following positions; stock has price 10, volatility 15%, riskfree rate 4%, time to expiration is 4 weeks;

    1. ATM call

    2. ATM put

    3. calls & puts with strike of 9.9, 9.8

    4. calls & puts with strike of 10.1, 10.2

  6. Get some option prices and find implied volatilities, then delta, gamma, and VaR, using reasonable assumptions about parameters.