A scaling limit for utility indifference prices in the discretised Bachelier model

Asaf Cohen; Yan Dolinsky

doi:10.1007/s00780-022-00473-y

A scaling limit for utility indifference prices in the discretised Bachelier model

Asaf Cohen, Yan Dolinsky^*

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider the discretised Bachelier model where hedging is done on a set of equidistant times. Exponential utility indifference prices are studied for path-dependent European options, and we compute their non-trivial scaling limit for a large number of trading times n and when risk aversion is scaled like nℓ for some constant ℓ> 0. Our analysis is purely probabilistic. We first use a duality argument to transform the problem into an optimal drift control problem with a penalty term. We further use martingale techniques and strong invariance principles and obtain that the limiting problem takes the form of a volatility control problem.

Original language	American English
Pages (from-to)	335-358
Number of pages	24
Journal	Finance and Stochastics
Volume	26
Issue number	2
DOIs	https://doi.org/10.1007/s00780-022-00473-y
State	Published - Apr 2022

Bibliographical note

Funding Information:
A. Cohen acknowledges the financial support of the National Science Foundation (DMS-2006305). Y. Dolinsky is supported in part by the GIF Grant 1489-304.6/2019 and the ISF grant 230/21.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

Asymptotic analysis
Path-dependent SDEs
Strong approximations
Utility indifference

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Cite this

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abstract = "We consider the discretised Bachelier model where hedging is done on a set of equidistant times. Exponential utility indifference prices are studied for path-dependent European options, and we compute their non-trivial scaling limit for a large number of trading times n and when risk aversion is scaled like nℓ for some constant ℓ> 0. Our analysis is purely probabilistic. We first use a duality argument to transform the problem into an optimal drift control problem with a penalty term. We further use martingale techniques and strong invariance principles and obtain that the limiting problem takes the form of a volatility control problem.",

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AB - We consider the discretised Bachelier model where hedging is done on a set of equidistant times. Exponential utility indifference prices are studied for path-dependent European options, and we compute their non-trivial scaling limit for a large number of trading times n and when risk aversion is scaled like nℓ for some constant ℓ> 0. Our analysis is purely probabilistic. We first use a duality argument to transform the problem into an optimal drift control problem with a penalty term. We further use martingale techniques and strong invariance principles and obtain that the limiting problem takes the form of a volatility control problem.

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A scaling limit for utility indifference prices in the discretised Bachelier model

Abstract

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Keywords

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