Derivatives -- the View from the Trenches

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Most of this sort of hocus-pocus was derived by Bruno Dupire in early 90s, but has received far too little recognition and attention in textbooks and academic circles. The French banks produce a lot of very good quants and they are all breed on a solid dose of Theorem 1 and all the corollaries. 12
Theorem 2: The Gospel of the Jump You can get a long way of understanding the world with Theorem 1, but there is one thing missing and that is jumps. Suppose the stock evolves according to dS() t () tdt() tdWt () ItdNt () () St ( ) where , are stochastic processes and N is a Poisson process with stochastic intensity () t , and the jump size is stochastic with distribution given by It ()~ (;) t Suppose we price according to the model dS() t dW () t I() t dN() t mdt St ( ) under Q , where Q QdNt [ ( ) 1] dt, It ( )~ (), mE [ It ( )] Theorem 2: A delta neutral trading book will accumulate gains at 1 ( 2 2 ) 2 Q SS [ ] dV S V dt VdN E V dt 2 Proof: Using the pricing equation 1 V mSV S V E V 2 2 2 Q 0 t S SS [ ] and Ito's lemma yields the result. 13
Page 1 and 2: Derivatives -- the View from the Tr
Page 3 and 4: My Life as a Quant CV: - 1997: PhD
Page 5 and 6: The First Fundamental Theorem of De
Page 7 and 8: Theorem 1 and Option Markets Black
Page 9 and 10: Theorem 1 and Models Theorem 1 ext
Page 11: Theorem 1 and Technical Results A
Page 15 and 16: But in essence the strategies invol
Page 17 and 18: Theorem 2 and the Equity Volatility
Page 19 and 20: So in front of you, you have an opt
Page 21 and 22: The Difference between P and Q and
Page 23 and 24: Model Philosophy Keep it simple --
Page 25 and 26: Foreign exchange - Black-Scholes wi
Page 27 and 28: An Interest Rate Model at Work in J

Derivatives -- the View from the Trenches

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