Derivatives -- the View from the Trenches

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The implied volatility gap in equities is a bit higher than in rates and fx. The reason for this is jumps but we will return to this. The difference in historical and implied volatility does not indicate that there is an arbitrage -- just that there is a risk premium on volatility. Ie, volatility is stochastic and market participants are risk averse. 8
Theorem 1 and Models Theorem 1 extends to other parameters such as for example correlation, and more sophisticated models than the constant volatility Black-Scholes model, generally 1 dV V dt 2 2 xx ( ) i j ij ij 2 ij , where ( x i ) are your risk factors and dxidx j ijdt . The general points is that if your model ,( ij) , is misspecified you are going to make daily Odt ( ) losses, not OdW ( ). So contrary to common belief: bad models cause bleeding -- not blow-ups. So it may take a while before you realise that your model is wrong. That is, you can pile up a lot of trades, make a lot of "model value", and many fine bonuses can be paid, before you realise that your book is bleeding. …and this has (involuntarily) been discovered by many banks: - UBS remark of IPS portfolio in the early 90s. - Commerzbank (and other's) remark of Bermudan swaption book in the late 90s. 9
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: Theorem 1 and Option Markets Black
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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