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Unformatted text preview: Introduction to derivatives, Fall 2011 BUSI 588, Final exam solutions Introduction to derivatives BUSI 588, Final Exam Solutions, Fall 2011 Problem 1 - Oratio Dominica (35 points) 1. The value of the put is $2.81. You would replicated it by shorting 0 . 3654 units of the underlying asset (note =- . 3654) as well as lending $21.08 (= 2 . 81- (- . 3654)50). You would have to short more of the underlying asset, lending out the proceeds. 2. From the basic forward pricing equation we have 1529 . 13 = 1500 1 . 05 (1 + ) , so the dividend yield is = 3%. By inspection, the puts and calls with a strike of $55 are particularly mispriced. The following is one particular strategy that yields arbitrage profits. Today In one-year S * < 55 S * 55 Buy put- 5 . 15 55- S * Buy asset- 50 S * S * Borrow PV of 55 +52 . 38- 55- 55 Sell call +2 . 95- ( S *- 55) Net . 18 Problem 2 - Fifty-cents (25 points) 1. The most direct way to approach this problem is via risk-neutral probabilities (i.e. normalized state prices). In our problem we had p u = r- d u- d = 1 . 01- . 6 1 . 4- . 6 = 0 . 5125; p d = 0 . 4875 . Starting at expiration we note that by basic principles the values of the put will be given by the following table. 8.53 3.45 0.00 0.00 14.05 7.14 0.00 21.60 14.80 29.20 2. This problem was intended to go through a dynamic replication argument in full At each date t , we look for a portfolio that buys t units of the stock, and invest B t dollars in the bond, so that t S tu + B t 1 . 01 = P tu ; t S td + B t 1 . 01 = P td ; c Diego Garc a, Kenan-Flagler Business School Page 1 of 4 Introduction to derivatives, Fall 2011 BUSI 588, Final exam solutions where S tu and P tu denote the prices of the underlying asset and the put in the up state (from node t ), and S td and P td denote the prices of the underlying asset and the put in the down state (from node t )....
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This note was uploaded on 11/25/2011 for the course BUSI 588 taught by Professor Staff during the Fall '10 term at UNC.
- Fall '10