Quizz3Ans(1) - Financial Risk Management Exercises Jos Da...

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Financial Risk Management Exercises. Jos´ e Da Fonseca email: [email protected] Auckland University of Technology First Name: Family Name: Id Number: Remark: the computations were performed in excel and copied in this file, you don’t need to report so many digits in your script. Exercise I (20 marks) t = 0 t = T 3 t = 2 T 3 t = T S % & uS dS % & % & u 2 S udS d 2 S % & % & % & u 3 S u 2 dS ud 2 S d 3 S with S = 1, u = 1 . 1, d = 0 . 9. We denote by t = 0 t = T 3 t = 2 T 3 t = T P % & P u P d % & % & P uu P ud P dd % & % & % & P uuu P uud P udd P ddd the evolution of a Put option with strike K , maturity T and we suppose that the rate (CC) is r = 2%. 1. (4 marks) Compute the price of this option with strike K = 1 . 0 and maturity T = 1. First, we build the tree for the stock: t = 0 t = T 3 t = 2 T 3 t = T 1 % & 1 . 1 0 . 9 % & % & 1 . 21 0 . 99 0 . 81 % & % & % & 1 . 331 1 . 089 0 . 891 0 . 729 For the option we obtain 1
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t = 0 t = T 3 t = 2 T 3 t = T 0 . 064195333 % & 0 . 023412197 0 . 11174585 % & % & 0 0 . 050516626 0 . 183355506 % & % & % & 0 0 0 . 109 0 . 271 2. (4 marks) Compute the evolution of the Delta along the tree. t = 0 t = T 3 t = 2 T 3 - 0 . 441668262 % & - 0 . 229621027 - 0 . 737993779 % & % & 0 - 0 . 550505051 - 1 3. (4 marks) Suppose that you sell one option at time t = 0 and you do not hedge, you keep the premium at the rate r .
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