hw4 - Derivative Securities, Fall 2007 Homework 4....

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Derivative Securities, Fall 2007 – Homework 4. Distributed 10/17/07, due 10/31/07. A solution sheet to HW3 will be posted 10/25; a solution sheet to HW4 will be posted 11/8; no late HW’s will be accepted once the corresponding solution sheet has been posted. 1. Let F solve the SDE dF = μF dt + σF dw , where μ and σ are constant and w is Brownian motion. Find the SDE solved by (a) V ( F ) = AF , where A is constant (b) V ( F ) = F (c) V ( F ) = cos F (d) V ( F,t ) = F 3 t 2 . 2. We continue to assume that F solves dF = μF dt + σF dw , where μ and σ are constant and w is Brownian motion. Find a function V ( F ) such that the process t 7→ V ( F ( t )) is a martingale (i.e. the SDE describing V ( F ) has no dt term). 3. This problem should help you understand Ito’s formula. If w is Brownian motion, then Ito’s formula tells us that z = w 2 satisfies the stochastic differential equation dz = 2 wdw + dt . Let’s see this directly: (a) Suppose a = t 0 < t 1 < .. . < t N - 1 < t
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This note was uploaded on 01/02/2012 for the course FINANCE 347 taught by Professor Bayou during the Fall '11 term at NYU.

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hw4 - Derivative Securities, Fall 2007 Homework 4....

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