Asymptotic analysis of hedging errors in models with jumps

Tankov, Peter; Voltchkova, Ekaterina

doi:10.1016/j.spa.2008.10.002

Cited by 38 publications

(24 citation statements)

References 18 publications

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“…Bertsimas, Kogan and Lo (2000), Hayashi and Mykland (2005) treated the same problem in the context of hedge-error. Tankov and Voltchkova (2009) extends the results to discontinuous semimartingales. Gobet and Temam (2001), Geiss (2002) among others gave asymptotic estimates in the L p sense under the Black-Scholes model.…”

Section: Introductionsupporting

confidence: 61%

Stochastic Analysis with Financial Applications

Kohatsu‐Higa¹,

Privault²,

Sheu³

2011

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Section: Introductionsupporting

confidence: 61%

Stochastic Analysis with Financial Applications

Kohatsu‐Higa¹,

Privault²,

Sheu³

2011

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“…Hayashi and Mykland (2005) use a weak convergence argument to derive the asymptotic distribution of the hedging error as the number of trades goes to infinity. Their approach was generalized by Tankov and Voltchkova (2009) to Le´vy processes with jumps. A very important problem, related to this, is that of determining a strategy that minimizes the variance of the hedging error.…”

Section: Introductionmentioning

confidence: 99%

Evaluating discrete dynamic strategies in affine models

Angelini

Herzel

2012

Quantitative Finance

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We consider the problem of measuring the performance of a dynamic strategy, re-balanced at a discrete set of dates, with the objective of hedging a claim in an incomplete market driven by a general multi-dimensional affine process. The main purpose of the paper is to propose a method to efficiently compute the expected value and variance of the hedging error of the strategy. Representing the payoff of the claim as an inverse Laplace transform, we are able to obtain semi-explicit formulas for strategies satisfying a certain property. The result is quite general and can be applied to a very rich class of models and strategies, including Delta hedging. We provide illustrations for the case of the Heston stochastic volatility model.

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“…We analyze this microstructure hedging error in two steps. First, we assume that there is no microstructure noise on the price but that the trading times are endogenous (for all i, P τ i = X τ i ): we expect results more or less similar to those in [2], [12], and [26], where exogenous trading times are considered. Second, we assume the presence of the endogenous microstructure noise and discuss the two hedging strategies.…”

Section: Asymptotic Distributions Of the Microstructural Hedging Errormentioning

confidence: 99%

On the Microstructural Hedging Error

Robert¹,

Rosenbaum²

2010

SIAM J. Finan. Math.

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Abstract.We consider the issue of hedging a European derivative security in the presence of microstructure noise. In a market where the efficient price of the asset is driven by a stochastic volatility process, we assume an agent wants to use a (possibly misspecified) local volatility-type replication strategy. Focusing on microstructure noise effects, our goal is to evaluate the error between the theoretical, but practically unfeasible, strategy and its market adapted versions. The microstructural hedging error is in particular due to transaction price discreteness and endogenous trading times. Thus, we consider a transaction price model that accommodates such inherent properties of ultrahigh frequency data with the assumption of a continuous semimartingale efficient price. In this framework, we study two hedging strategies derived from the local volatility-type hedging strategy: (i) the hedging portfolio is rebalanced every time that the transaction price moves; (ii) the hedging portfolio is rebalanced only once the transaction price has varied by more than a selected value. To assess these strategies, we use an asymptotic approach where the number of rebalancing transactions goes to infinity. For the first strategy, we show that, because of microstructure noise effects, the hedging error does not vanish. However, an optimal strategy of the second type enables us to reduce it significantly.

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Asymptotic analysis of hedging errors in models with jumps

Cited by 38 publications

References 18 publications

Stochastic Analysis with Financial Applications

Stochastic Analysis with Financial Applications

Evaluating discrete dynamic strategies in affine models

On the Microstructural Hedging Error

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