Derivatives -- the View from the Trenches

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- Interest rate option problems at NatWest (and other places) in mid 90s. - Several banks' current problem with exotic equity option books. - … All sad examples of taking it a bit too easy on the model front. 10
Theorem 1 and Technical Results A lot of technical results can be derived from the Theorem 1: For example, set 0 and let then 1 Vt () ln St () St () St () logcontract priced at 0 delta hedge of logcontract at 0 1 T T 2 1 ln ST ( ) ln S(0) ( ) ( ) 2 u du dSu 0 0 Su ( ) Hence a contract paying the realised variance can be replicated with a simple delta strategy combined with a contract paying ln ST ( ) , which in turn can be statically replicated with positions in European options. Another example is 0 and Vt () ( St () K) 1 St () call option priced at 0 St () K delta hedge of call option at 0 Theorem 1 and a few manipulations yield E t S t K Q 2 [ ( ) | ( ) ] 2 C ( T, K) K C ( T, K) T 2 KK where Q CT ( , K) E [( ST ( ) K) ] 11
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: Theorem 1 and Models Theorem 1 ext
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

Derivatives -- the View from the Trenches

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