FINM345A09Homework9 - FINM345/STAT390 Stochastic Calculus...

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Unformatted text preview: FINM345/STAT390 Stochastic Calculus – Hanson – Autumn 2009 Lecture 9 Homework (HW9): Stochastic Volatility (Due by Lecture 10 in Chalk FINM345 Assignment Submenu) { Note: Dropped the Digital Dropbox } You must show your work, code and/or worksheet for full credit. There are 10 points per question if best correct answer and negative points for missing homework sets. Corrections are in Red as are comments, November 27, 2009 1. Show that the nonsingular, explicit, exact solution [L9-p16:(9.13)], V ( t )= e- κ v ( t ) p V +0 . 5 Z t e κ v ( s ) / 2 ( σ v dW v )( s ) 2 , (1) when σ 2 v ( t ) = 4 κ v ( t ) θ v ( t ) ∀ t , is a solution satisfying the mean-reverting, square-root diffusion [L9-p16:(9.2)], dV ( t )= κ v ( t )( θ v ( t )- V ( t )) dt + σ v ( t ) p V ( t ) dW v ( t ) , V (0)= V > , (2) by the Itˆ o calculus or by increment expansion of V ( t ) solution (9.13) in the limit of dt –precision....
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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.

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