Derivatives - Final Exam Solutions

Econ 724-01 Financial Derivatives I Final Examination Instructions: 1. The test is open-book and open-notes. 2. Time allowed: 4 hours 1. Refer to the data in Table 1. a)

Lau Spring 2011

Suppose you long 10 June 2011 British Pound contracts on April 26, 2011 (T) (at the settlement price) and you close your position on April 27, 2011 (W) (at the settlement price), how much will you make/lose? Suppose you long 10 June 2011 British Pound contracts on April 27, 2011 (W) at the open and you close your position on April 27, 2011 (W) (at the settlement price), how much will you make/lose?

b)

2.

Based on the data in the following table, compute the  of the May11 131 Call. 4/25/11 4/26/11 SPY $133.64 $104.79 SPY May11 131 Call $3.58 $4.36

3.

(15 points) A corporate client wants to borrow $1,000,000 from a bank. A bank offers a corporate client 3 different loans plans: a) borrowing $1,000,000 cash at 12% per annum with annual compounding, b) borrowing 1000 ounces of gold (the spot price of gold is $1000 per ounce) at 2.5% per annum with annual compounding, (if gold is borrowed, interest must be repaid in gold), and c) borrowing £ 500,000 (the spot price of £ is 1£  $2 ) at 10% per annum with annual compounding. Suppose rUS  9%, r£  8%, and u  1% per annum (with continuous compounding). Explain in detail which loan plan the corporate client should choose.

4.

(20 points) A non-dividend-paying stock with a volatility of 30% per annum is currently trading at $60. Let r  4% . a) Using the 1-step binomial tree model, calculate the value of a 6-month European put option with X  $75 b) Using the 2-step binomial tree model, calculate the value of a 6-month American put option with X  $75 .

1

5.

(20 points) Suppose S (current stock index)  1600, r  10%,   20%, and q  4% . An investor has a portfolio which is worth $10,000,000 with   2 . Suppose the investor wants to protect the value of his/her portfolio at the current level (i.e.