UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Actuarial Science Program
DEPARTMENT OF MATHEMATICS
Math 476 / 567 Prof. Rick Gorvett
Actuarial Risk Theory Fall, 2008
Homework Assignment # 5 (max. points = 10)
Due at the beginning of class on Thursday, October 16, 2008
You are encouraged to work on these problems in groups of no more than 3 or 4. However, each
student must hand in her/his own answer sheet. Please show your work – enough to show that
you understand how to do the problem – and circle your final answer. Full credit can only be
given if the answer and approach are appropriate. Please provide answers to two decimal places.
Note: When calculating a percentage, please provide answers either as a proportion to
four decimal places (e.g., 0.xxxx), or as a percentage to two decimal places (e.g., xx.xx%).
(1) Consider a call option and a put option to exchange a share of ABC stock (the underlying
asset) and a share of XYZ stock (the strike asset). Both options are European, and have
expiration dates nine months from now. Both ABC and XYZ stock pay continuous
dividends at the rate (dividend yield) of 2% per year. The current price of the call is
$3.50, the current price of a share of ABC stock is $80, and the current price of XYZ
stock is $83. Find the price of the exchange put option.
(2) Consider a European 60-strike call option on 100 shares of ABC stock. You believe that,
on the expiration date of the option, the stock price is equally likely to be anywhere
between $30 and $70 per share. What is the expected payoff of the call option?
(3) Same question as problem (2) above, except that you believe that the per-share stock
price S will have the following distribution on the call expiration date:
1
0.0025s – 0.075, 30≤s≤50
f(s) =
0.175 – 0.0025s, 50≤s≤70
For problems (4) and (5), use the 1,000 random numbers between 0 and 1, located in the
hw5.xls spreadsheet which is linked to the class website. Using the inverse transform
method, use these random numbers to simulate 1,000 possible values of an underlying
asset (i.e., stock price) on the expiration date of some European options. Assume the
stock prices follow a normal distribution with a mean of 100 and a standard deviation of
20. Use the =NORMINV function in Excel.
