Derivatives -- the View from the Trenches

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Theorem 1 and Trading If you're gamma long, VSS 0, and realised volatility is higher than pricing volatility you make money. The option trader's job is really about balancing realised against implied (or pricing) volatility. realised vol > implied vol => go long gamma realised vol < implied vol => go short gamma In essence this is what all trading is about: buy low -- sell high. In practice it is of course not that easy to predict how realised and implied volatility are going to relate to each other over a given period. In the context of the derivation of the Black-Scholes' formula, one can see Theorem 1 as an investigation of the selffinancing condition. 6
Theorem 1 and Option Markets Black-Scholes implied volatility has to satisfy 1 E u S u V u du 2 Q T 2 2 2 [ ( ( ) ) ( ) ( ) ] 0 0 implied SS So implied volatility is a weighted average of Q expected volatility. Consider an option seller that delta hedges his short option position, i.e. VSS 0, with the implied volatility. His total profit 1 T 2 2 2 VT ( ) V(0) ( ( ) ) ( ) ( ) 2 t 0 implied St VSS tdt is positive if implied () t "most of the time". If option sellers are risk averse (and they are) it is unlikely that they are willing to be short gamma without taking a premium. We should expect implied volatility > historical volatility Implied volatility gaps for big ccys and index - Rate options: 0.5-1.0% - Equity options: 3.0-5.0% - Foreign exchange: 0.5-1.0% 7
Page 1 and 2: Derivatives -- the View from the Tr
Page 3 and 4: My Life as a Quant CV: - 1997: PhD
Page 5: The First Fundamental Theorem of De
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

Derivatives -- the View from the Trenches

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