GT_Atlanta_07052011

GT_Atlanta_07052011 - Issues in option pricing Modeling...

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Unformatted text preview: Issues in option pricing Modeling dependence Risk neutral pricing Results Merton Jump-Diffusion Revisited: A L evy Copula Approach Pierre Garreau 1- Craig Nolder 5 th Annual Graduate Student Conference in Probability April 29 - May 01, 2011 1 Financial Mathematics, Florida State University 1 / 29 Merton Jump-Diffusion Revisited: A L evy Copula Approach Issues in option pricing Modeling dependence Risk neutral pricing Results 1 Issues in option pricing 2 Modeling dependence 3 Risk neutral pricing 4 Results 2 / 29 Merton Jump-Diffusion Revisited: A L evy Copula Approach Issues in option pricing Modeling dependence Risk neutral pricing Results The Black-Scholes syndrom 20 40 60 80 100 120 140 160 180 200 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 SPX Black-scholes diffusion: dS t = S t ( rdt + dW t ) 3 / 29 Merton Jump-Diffusion Revisited: A L evy Copula Approach Issues in option pricing Modeling dependence Risk neutral pricing Results The Black-Scholes syndrom 20 40 60 80 100 120 140 160 180 200 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 SPX Black-scholes diffusion: dS t = S t ( rdt + dW t ) Pricing - Arbitrage Theory / Feynman-Kac: P ( t , x ) = E Q bracketleftBig f ( tildewide S t , x T ) |F t bracketrightBig Hedging - Martingale representation theorem: V t = c + integraldisplay t s d tildewide S s , Q a . s . 3 / 29 Merton Jump-Diffusion Revisited: A L evy Copula Approach Issues in option pricing Modeling dependence Risk neutral pricing Results The Black-Scholes syndrom 20 40 60 80 100 120 140 160 180 200 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 S P X 0.2 0.4 0.6 0.8 1-0.05 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Black-scholes diffusion: dS t = S t ( rdt + dW t + dq t ) Pricing - Arbitrage Theory / Feynman-Kac: P ( t , x ) = E Q bracketleftBig f ( tildewide S t , x T ) |F t bracketrightBig Hedging - Martingale representation theorem: V t = c + integraldisplay t s d tildewide S s , Q a . s . 3 / 29 Merton Jump-Diffusion Revisited: A L evy Copula Approach Issues in option pricing Modeling dependence Risk neutral pricing Results The Black-Scholes syndrom 900 1000 1100 1200 1300 1400 1500 1600 0.2 0.4 0.6 0.8 900 1000 1100 1200 1300 1400 1500 1600 0.5 1 1.5 2 600 650 700 750 800 850 900 950 0.2 0.4 0.6 0.8 600 650 700 750 800 850 900 950 0.5 1 1.5 2 * = C- 1 ( K , S , T , r ) , C ( K , S , T , r ) = N ( d t , 1 ) e k t N ( d t , 2 ) 4 / 29 Merton Jump-Diffusion Revisited: A L evy Copula Approach Issues in option pricing Modeling dependence Risk neutral pricing Results Risk neutral in two dimensions 0.05 0.1 0.15 0.2-2.5-2-1.5-1-0.5 0.5 1 1.5 2 Q 1 d S 1 t / S 1 t = 1 dB 1 t Q 2 d S 2 t / S 2 t = 2 dB 2 t P 1 ( t , x ) = E Q 1 bracketleftBig f ( tildewide S 1 , x T ) |F t bracketrightBig P 2 ( t , x ) = E Q 2 bracketleftBig f ( tildewide S 2 , x T ) |F t bracketrightBig 5 / 29 Merton Jump-Diffusion Revisited: A L evy Copula Approach Issues in option pricing...
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This note was uploaded on 01/15/2012 for the course MAT 5939 taught by Professor Garreau during the Fall '11 term at FSU.

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GT_Atlanta_07052011 - Issues in option pricing Modeling...

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