Homework 7

due April 29 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 put option on a stock has strike of 75; the current price of the stock is 78.50.  The riskfree rate is 3%, time to expiry is 45 days, and the volatility is 17%. 
    1. What is the Black-Scholes implied value?  
    2. What is the value of a call with same characteristics? 
    3. Does put-call parity hold?
    4. If the price of the stock falls to 77.5, how much do the call and put prices change?  What does this imply about the delta of the call and put?  Using the formula, what is the delta and gamma for each?
  2. In class we discussed hedging a portfolio of SPX contracts with options on that index.  Calculate the implied volatilities for those option prices, with riskfree rate from LIBOR (look it up!), assume q=2%, S0 = 1192.13 and T=35 days. 

K=

p=

925

.75

950

.95

975

1.10

1000

1.60

1025

2.10

1050

2.70

1075

3.50

1100

5.00

1125

7.5

1150

10.7

1175

17.4

1200

26

Find payoffs to the fund, if you bought different put options.  Which do you think offers the best set of risks?

  1. A set of options mature in 2 months.  The stock has volatility of 32%.  LIBOR is 3%.  The current market price of the underlier is 25.  It pays dividends at a continuous rate of 1%. 
    1. What is the price of a bull spread, with strikes of 24 and 26, using the B-S-M model?
    2. If the security paid no dividends, what would be the cost of a bull spread?  Is it more or less costly?  Why?
  2. Consider the prices of currency options on the "zing" (the currency of Zembla).  Zemblan interest rates are at 2% while US riskfree rates are 1%.  The zing trades at 10 zing/$ today; its volatility is 20%.  What is the cost of an ATM straddle, expiring in 3 months, as implied by B-S-M model?  Would the cost be more or less, for an ATM straddle expiring in 6 months?  If the zing suddenly became more volatile?