# Quiz3b - Financial Risk Management Exercises Jos Da Fonseca...

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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 with maturity T = 1 and we suppose that the rate (CC) is r = 0%. At maturity the payoff of the option is given by: 0 . 5 if S T > 1 . 2 1 . 0 if S T [1 . 0 1 . 2] 0 . 5 if S T [0 . 85 1 . 0] 0 if S T < 0 . 85 1. (2 marks) Compute the price of this option. 2. (2 marks) Compute the evolution of the Delta along the tree. 3. (2 marks) Suppose that you sell an option and you do not hedge but invest the premium at the rate r . What is your global position at the maturity of the option? Why it is problematic from a risk management point of view? 4. (3 marks) Suppose that you sell one option and you hedge by taking the delta position computed at time t = 0. Instead

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