Hedging with Stochastic and Local Volatility
AbstractWe derive the local volatility hedge ratios that are consistent with a stochastic instantaneous volatility and show that this ‘stochastic local volatility’ model is equivalent to the market model for implied volatilities. We also show that a common feature of all Markovian single factor stochastic volatility models, (log)normal mixture option pricing models and ‘sticky delta’ models is that they predict incorrect dynamics for implied volatility. As a result they over-hedge the Black-Scholes model in the presence of a market skew and this explains the poor delta hedging performance of these models reported in the literature. Whilst the traditional ‘sticky tree’ local volatility models do not possess this unfortunate property, they cannot be used for pricing without exogenous and ad hoc smoothing of results. However the stochastic local volatility framework allows one to extend a good pricing model into a good hedging model. The theoretical results are supported by an empirical analysis of the hedging performance of seven models, each with different volatility characteristics, on the SP500 index skew.
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Bibliographic InfoPaper provided by Henley Business School, Reading University in its series ICMA Centre Discussion Papers in Finance with number icma-dp2004-10.
Length: 47 pages
Date of creation: Jul 2004
Date of revision: Dec 2004
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Local volatility; stochastic volatility; implied volatility; hedging; dynamic delta hedging; volatility dymamics;
Find related papers by JEL classification:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
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