Quizz3bAns - 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: 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 C % & C u C d % & % & C uu C ud C dd % & % & % & C uuu C uud C udd C ddd the evolution of an option. We suppose that the payoff is given by C uuu = 0, C uud = 0 . 25, C udd = 0 . 5 and C ddd = 0, maturity T and we suppose that the rate (CC) is r = 2%. 1. (4 marks) Compute the price of this option 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 . 268328222 % & 0 . 230187929 0 . 315783619 % & % & 0 . 115863821 0 . 364202698 0 . 264950111 % & % & % & 0 0 . 25 0 . 5 0 2. (4 marks) Compute the evolution of the Delta along the tree. t = 0 t = T 3 t = 2 T 3 - 0 . 42797845 % & - 1 . 128813075 0 . 55140326 % & % & - 1 . 033057851 - 1 . 262626263 3 . 086419753 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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