Assignment 1 - Introduction to Computational Finance | CSCI 6961, Assignments of Computer Science

Download Assignment 1 - Introduction to Computational Finance | CSCI 6961 and more Assignments Computer Science in PDF only on Docsity! CSCI 6961 RPI Introduction to Computational Finance Fall 2008 ASSIGNMENT 1, due Thursday, September 11 Homeworks are due at the begining of class or in my mail box by 2pm on the due date. The point value for the 6000 level is indicated in small font. 1 (50 (25) points) Bonds and Arbitrage (a) [20 (10)] A coupon paying bond gives coupon payments of X1, X2, . . . , Xn at times t1, t2, . . . , tn and a final principal payment of F at time T . Use an arbitrage argument to show that the price of this bond today should be P = n∑ i=1 XiB(0, ti) + F · B(0, T ), where B(0, t) is the usual zero coupon bond. Rewrite this formula in terms of the interest rate, r, which you can assume is a constant. (b) [20 (10)] On the website for this problem set, you can download zero coupon bond data in the file zero coupon.dat. This data was obtained from www.bondtrac.com on 09/02/05. This file contains five columns, the first three are the month, day and year of expiry of the bond. The fourth is the time to expiry in years, T , and the fifth is the price of the bond, B(0, T ). The value of the payment (face value) at time T is $100, not $1 as discussed in class. Note that some dates are repeated because typically data is collected from multiple sources. You need to deal with this issue. (i) Give a plot of B(0, T ) versus T and explain the general observed shape. (ii) Using the prices and times to expiry, obtain the implied interest rate to that time. Plot the implied interest rate as a function of T . Is this curve a constant? If not, suggest explanations for why not. (c) [10 (5)] Using the zero coupon bond data, price the following contract. I will pay you $1 on 02/15/2006 in return for $2 on 08/15/2009 2 (0 (25) points) Bond Portfolio Immunizartion Exercise 2.10 in the notes. 1