Homework 6

due April 15 (along with your taxes) Thursday

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

 

 

You are encouraged to form study groups to work on these problems.  However each student must hand in a separate assignment: the group can work together to discuss the papers and comment on drafts, but each study group member must write it up herself/himself.  When emailing assignments, please include your name and the assignment number as part of the filename.

Please write the names of your study group members at the beginning of your homework to acknowledge their contributions.

  1. A certain security is currently worth $23.  Its annualized volatility is 25%. LIBOR is 0.045. 
    1. To value a call option that matures in 5 months with a strike price of 25,what price would be implied by the Black-Scholes-Merton model? 
    2. A put option with the same strike? 
    3. Is put-call parity satisfied?
    4. What if you used a one-step tree model -- how much different are the valuations?  (Remember that Hull suggested a link between volatility and step size.)

 

  1. You are overseeing a new portfolio manager, who currently has a $50,000 in shares of stock in Mega Corp (price of 37, 40% volatility).  The new portfolio manager plans to write (i.e. take a short position in) 1300 calls with a strike of 38 expiring in 9 months and to write (i.e. take a short position in) 13000 puts with a strike of 35 expiring in 9 months.  (Your company reports annual results in 10 months, thus the managers are focused on getting good returns over that horizon.)  Assume LIBOR is 3%.  The new portfolio manager says that the positions are an excellent hedge.  Investigate whether this is correct.
    1. What are the Black-Scholes-Merton (BSM) prices for the call and put (how much is the bank getting for writing these)?
    2. If, after 4 months, the stock price has gone up to 40, what are now the BSM prices?
    3. If, instead, after 4 months, the stock price has gone down to 35, what are now the BSM prices?
    4. Evaluate the claims that this portfolio is hedged.  (Assume that Mega Corp's beta with market returns is 80%.)