Arbitrage in Multi-Period Economies: Computational Finance Assignment 4, Assignments of Computer Science

Download Arbitrage in Multi-Period Economies: Computational Finance Assignment 4 and more Assignments Computer Science in PDF only on Docsity! CSCI 6961 RPI Introduction to Computational Finance Fall 2008 ASSIGNMENT 4, due Thursday, October 16 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 (35 (25) points) Arbitrage - Two Period Consider the following two period economies. Determine (to within reasonable precision) which ones have arbitrage opportunities. If you think that an economy has an arbitrage opportunity, give the portfolio that results in the arbitrage opportunity. If you believe that there is no arbitrage opportunity, then give the risk neutral probabilities (or the Martingale measure). Note, sometimes the risk neutral probabilities may not be unique. In all cases, justify your answer. We use S to denote the current instrument prices, and Z to denote the future instrument price matrix. (a) (i) S1 =     5 14 20 33.5     Z1 =     14 5 5 10 12 17 10 17 25 10 9 8     (ii) S2 =     5.47 14 20 8.825     Z2 =     14 5 5 10 12 17 10 17 25 10 9 8     (b) (i) S1 = [ 15 10 ] Z1 = [ 14 5 5 10 12 17 ] (ii) S2 = [ 8 13 ] Z2 = [ 14 5 5 10 12 17 ] 2 (15 (25) points) Arbitrage - Multi-Period Consider the following stock dynamics according to our binomial model with probability p. 1