Derivatives -- the View from the Trenches

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Career highlights - Solved the passport option problem and implemented the world's first live model. Did 10 trades. - Developed Gen Re's Japanese "Power Reverse Dual" business. 350 20-30y trades on 40 Pentium CPUs. Takes 6h to run risk reports. - Sorted out the modeling of Band of America's 1500 trade portfolio of Bermudan swaptions. - 2001 Risk Magazine Quant-of-the-Year. Career the-opposite - Realising my first ever serious screw up (USD -450,000). - Warren Buffet closing down Gen Re Finanical Products. Purpose of this talk: to entertain with what I've learned so far. 4
The First Fundamental Theorem of Derivatives Trading We assume zero rates and dividends and standard frictionless markets. Assume that the underlying stock evolves continuously. So there exists two stochastic processes , so that dS() t () tdt() tdWt () St () under the real measure P . Let V be the value of an option book on S priced on a model with constant volatility . Assume that the book is delta hedged, i.e. we dynamically trade the stock to keep V 0 S Theorem 1: The value of the option book evolves according 1 dV t t S t V t dt 2 2 2 () ( () ) () SS () 2 Proof: Follows from V V(, t S()) t and Ito's lemma that 1 dV Vtdt VSdS VSSdS 2 1 2 2 Vdt t VSS S dt 2 1 2 2 Using 0 Vt S VSS we get the result 2 2 5
Page 1 and 2: Derivatives -- the View from the Tr
Page 3: My Life as a Quant CV: - 1997: PhD
Page 7 and 8: Theorem 1 and Option Markets Black
Page 9 and 10: Theorem 1 and Models Theorem 1 ext
Page 11 and 12: Theorem 1 and Technical Results A
Page 13 and 14: Theorem 2: The Gospel of the Jump
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

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