Model-free hedge ratios and scale-invariant models

Alexander, Carol; Nogueira, Leonardo M.

doi:10.1016/j.jbankfin.2006.11.011

Cited by 64 publications

(60 citation statements)

References 51 publications

(76 reference statements)

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“…For the Heston model, which is employed in the empirical study, Theorem 1 in Cheridito, Filipovic & Kimmel (2007) shows that the martingale property holds if the Feller condition is satisfied under both the original measure and the minimal martingale measure. more on risk-minimizing delta hedges for exotic options we refer the reader to Alexander & Nogueira (2007a). For the stochastic volatility model, the steps work out like this.…”

Section: (2)mentioning

confidence: 99%

Risk Minimization in Stochastic Volatility Models: Model Risk and Empirical Performance

2007

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In this paper the performance of locally risk-minimizing delta hedge strategies for European options in stochastic volatility models is studied from an experimental as well as from an empirical perspective. These hedge strategies are derived for a large class of diffusion-type stochastic volatility models, and they are as easy to implement as usual delta hedges. Our simulation results on model risk show that these risk-minimizing hedges are robust with respect to uncertainty and misconceptions about the underlying data generating process. The empirical study, which includes the U.S. sub-prime crisis period, documents that in equity markets risk-minimizing delta hedges consistently outperform usual delta hedges by approximately halving the standard deviation of the profit-and-loss ratio.

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confidence: 99%

Risk Minimization in Stochastic Volatility Models: Model Risk and Empirical Performance

2007

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“…The reason for this is that its price hedge ratios are theoretically equivalent to the standard (partial derivative) price hedge ratios derived from any proper model for pricing options on a tradable asset, which are well‐known to perform poorly relative to the implied BSM. See Alexander and Nogueira () for further details . By contrast, local volatility (sticky tree) delta‐hedges are usually more effective than implied BSM deltas, except possibly for hedging high‐strike options with frequent rebalancing…”

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confidence: 99%

“…Alexander and Nogueira () extended and formalized the concept of scale invariance, first introduced by Merton (). An option‐pricing model is scale invariant if and only if the relative change of the futures price is independent of the price level.…”

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confidence: 99%

“…The sticky moneyness model is also referred to as the “sticky delta” model. Its delta is the scale‐invariant delta defined by Alexander and Noguiera (), which is a partial price derivative hedge ratio that is model‐free in the class of scale‐invariant models. Hence, SM deltas include, for example, the partial derivative deltas of the Heston () model and of any deterministic volatility function (e.g.…”

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confidence: 99%

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Regime‐dependent smile‐adjusted delta hedging

Alexander¹,

Rubinov²,

Kalepky³

et al. 2011

Journal of Futures Markets

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We introduce several regime-dependent smile-adjusted deltas and compare their efficiency with the smile-adjusted deltas that are popular with option traders. Using years of daily option prices, out-of-sample hedging performance tests for options of all moneyness and maturities and daily, weekly, or fortnightly rebalancing show that even the simplest regime-dependent smile-adjustment consistently outperforms implied BSM delta hedging and local volatility and minimum variance smile-adjustments. Markov-switching deltas offer the best performance, with delta-hedging errors often half the size of implied BSM hedging errors. During volatile markets risk reduction from regime-dependent delta hedging is much greater than during tranquil periods

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“…Another way to view these results is to consider the results of Bates (2005) and Alexander and Nogueira (2005). Essentially, for any contingent claim that is homogenous of degree one, option partial derivatives with respect to the underlying can be computed, model-free, by taking partial derivatives of option prices with respect to strike prices.…”

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confidence: 99%