Tut3 - ACTSC/STAT 446/846 Tutorial #3 April 1st, 2009 Let W...

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Unformatted text preview: ACTSC/STAT 446/846 Tutorial #3 April 1st, 2009 Let W = { W t ,t } be a P-Brownian motion. 1. Find a measure e P under which t + W t is a (possibly non-standard) Brownian motion. 2. Assume that S = { S t ,t } follows Black-Scholes model. Compute the premium of the following payoffs: (a) S T ; (b) S T/ 2 ; (c) S T S k ; (d) max { S T ,K } ; (e) 10 I { S T > 110 } + 2 I { S T 110 } ; 3. In Black-Scholes model, compute the time- price of the following geometric Asian option , that is the option with payoff ( S 1 S 2 S 3 ) 1 / 3 at its maturity date T = 3 . Is this premium larger/smaller than the premium of an otherwise identical arithmetic Asian option ? 4. A binary call is a contract that pays $1 at the expiry time T if the asset price at that time is greater than the exercise price K , and zero otherwise. Let r be the continuously compounded interest rate. Assuming that the price of a risky asset S follows a geometric Brownian motion with volatility , find closed-form expressions for the price of a binary call at time 0 and the delta of this option. 5. In the framework of Black-Scholes model, assume that the risky asset models the Dow Jones index with an instantaneous volatility of 15% , an initial value of $20 and that the risk-free rate is 10% . An insurance company sells an index-linked contract with maturity T = 1 year for $1000....
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This note was uploaded on 01/16/2011 for the course ACTSC actsc 446 taught by Professor Idk.. during the Spring '09 term at Waterloo.

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Tut3 - ACTSC/STAT 446/846 Tutorial #3 April 1st, 2009 Let W...

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