Homework 8 – last one!

due May 6 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. Please complete Assignment Question 20.17 in Hull.
  2. Consider options on euros – which are quite volatile because of Greece.  The euro-linked contract traded for 133.95.  Options were traded at strikes and prices given in the table below.  Figure out the implied volatility of each option.  What is the delta and gamma of each?  If you had a portfolio that was long in each option, what would be the VaR?  (Extra: can you find a cheaper portfolio with a lower VaR?)

Calls

Last

Strike

implied volatility

delta

gamma

put

0.44

124

put

0.27

125

put

0.35

126

put

0.57

127

put

1.21

130

put

1.6

132

put

1.85

132.5

call

3.32

134.5

call

2.06

135

call

1.21

137

call

1

139

call

0.12

146

call

0.2

148

call

0.11

150.5

 

  1. A stock in the "ACME Corp" (monopoly suppliers of cartoon tools!) has 30% volatility over a year. ACME's current price is 10. Your portfolio is long with 100,000 shares of the stock (bought at 10), long 40 contracts (each on 1000 shares) of puts with strike prices of 7, 8 and 9 (expiring in 3 weeks) and long 50 contracts of a call with a strike price of 11, which has one month to expiry.  A riskless bond pays 2% per year (compounded continuously). 
    1.  Assuming Black-Scholes-Merton holds, calculate the portfolio value.
    2. What is the portfolio delta?
    3. What is the portfolio's 1% one-day VaR?  Its 5%?
    4. You consider adding a contract of a call on the index (index currently trades at 1000; each index contract is equivalent to 100 times the index; the call has K=1050; the index volatility is 12%).  If ACME has a beta of 0.75 with the index, what is now the portfolio delta?  What is the portfolio's 1% and 5% one-day VaR?

What a great exam question!  It wraps up everything!

  1. Please complete Assignment Question 22.28 in Hull.
  2. Please complete Assignment Question 23.28 in Hull.