# Quizz3b(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: 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. 2. (4 marks) Compute the evolution of the Delta along the tree. 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
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Unformatted text preview: r . What is you global position at time T (depending on the stock value at that date)? 4. (8 marks) Suppose that you sell one option at time t = 0 and you take a position on the stock equals to the Delta Δ (at that date t = 0). Describe the trades you perform at time t = 0 to build your hedging portfolio. We suppose that you keep the delta position chosen at time t = 0 along the tree, that is to say do not perform a dynamic hedging. What is your global position at time T depending on the stock value at that date? 1...
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