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Unformatted text preview: FINM345/STAT390 Stochastic Calculus – Hanson – Autumn 2009 Lecture 3 Homework: Stochastic Jump and Diffusion Processes (Due by Lecture 4 in Chalk FINM345 Digital Dropbox) You must show your work, code and/or worksheet for full credit. There are 10 points per question if correct answer. Corrections are in Red , October 14, 2009 1. Finance Oriented Martingales. A martingale in continuous time satisfies the essential property that E[ M ( t ) | M ( s )] = M ( s ) , for all 0 ≤ s < t provided its absolute value has finite expectation, i.e., E[ | M ( t ) | ] < ∞ for all t ≥ 0, plus some other technical properties. (a) Show that M 1 ( t ) = ln( X ( t ))- E[ln( X ( t ))] is a martingale where Y ( t ) = ln( X ( t )) symbolically satisfies the solution to the general linear diffusion SDE transformed to state-independent SDE form (E.g., (3.3) on L3-54 or (4.25) in text). 2. Exponential-Martingale Counterexample to Simple Notion that Martin- gales are always Driftless, a common stochastic finance legend.gales are always Driftless, a common stochastic finance legend....
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This note was uploaded on 04/19/2010 for the course FIN 390 taught by Professor Hansen during the Fall '09 term at University of Illinois, Urbana Champaign.
- Fall '09