Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis

Yuan Hu; W. Brent Lindquist; Svetlozar T. Rachev; Abootaleb Shirvani; Frank J. Fabozzi

doi:10.1016/j.jedc.2022.104345

Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis

Yuan Hu, W. Brent Lindquist, Svetlozar T. Rachev, Abootaleb Shirvani, Frank J. Fabozzi

Mathematics and Statistics

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

Abstract

Applying the Cherny-Shiryaev-Yor invariance principle, we introduce a generalized Jarrow-Rudd (GJR) option pricing model with uncertainty driven by a skew random walk. The GJR pricing tree exhibits skewness and kurtosis in both the natural and risk-neutral world. We construct implied surfaces for the parameters determining the GJR tree. Motivated by Merton's pricing tree incorporating transaction costs, we extend the GJR pricing model to include a hedging cost. We demonstrate ways to fit the GJR pricing model to a market driver that influences the price dynamics of the underlying asset. We supplement our findings with numerical examples.

Original language	English
Article number	104345
Journal	Journal of Economic Dynamics and Control
Volume	137
DOIs	https://doi.org/10.1016/j.jedc.2022.104345
State	Published - Apr 2022

Keywords

Cherny-Shiryaev-Yor invariance principle
Hedging transaction cost
Jarrow-Rudd binomial option pricing
Skew random walk

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10.1016/j.jedc.2022.104345

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title = "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis",

abstract = "Applying the Cherny-Shiryaev-Yor invariance principle, we introduce a generalized Jarrow-Rudd (GJR) option pricing model with uncertainty driven by a skew random walk. The GJR pricing tree exhibits skewness and kurtosis in both the natural and risk-neutral world. We construct implied surfaces for the parameters determining the GJR tree. Motivated by Merton's pricing tree incorporating transaction costs, we extend the GJR pricing model to include a hedging cost. We demonstrate ways to fit the GJR pricing model to a market driver that influences the price dynamics of the underlying asset. We supplement our findings with numerical examples.",

keywords = "Cherny-Shiryaev-Yor invariance principle, Hedging transaction cost, Jarrow-Rudd binomial option pricing, Skew random walk",

author = "Yuan Hu and Lindquist, {W. Brent} and Rachev, {Svetlozar T.} and Abootaleb Shirvani and Fabozzi, {Frank J.}",

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doi = "10.1016/j.jedc.2022.104345",

language = "English",

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AU - Hu, Yuan

AU - Lindquist, W. Brent

AU - Rachev, Svetlozar T.

AU - Shirvani, Abootaleb

AU - Fabozzi, Frank J.

PY - 2022/4

Y1 - 2022/4

N2 - Applying the Cherny-Shiryaev-Yor invariance principle, we introduce a generalized Jarrow-Rudd (GJR) option pricing model with uncertainty driven by a skew random walk. The GJR pricing tree exhibits skewness and kurtosis in both the natural and risk-neutral world. We construct implied surfaces for the parameters determining the GJR tree. Motivated by Merton's pricing tree incorporating transaction costs, we extend the GJR pricing model to include a hedging cost. We demonstrate ways to fit the GJR pricing model to a market driver that influences the price dynamics of the underlying asset. We supplement our findings with numerical examples.

AB - Applying the Cherny-Shiryaev-Yor invariance principle, we introduce a generalized Jarrow-Rudd (GJR) option pricing model with uncertainty driven by a skew random walk. The GJR pricing tree exhibits skewness and kurtosis in both the natural and risk-neutral world. We construct implied surfaces for the parameters determining the GJR tree. Motivated by Merton's pricing tree incorporating transaction costs, we extend the GJR pricing model to include a hedging cost. We demonstrate ways to fit the GJR pricing model to a market driver that influences the price dynamics of the underlying asset. We supplement our findings with numerical examples.

KW - Cherny-Shiryaev-Yor invariance principle

KW - Hedging transaction cost

KW - Jarrow-Rudd binomial option pricing

KW - Skew random walk

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DO - 10.1016/j.jedc.2022.104345

M3 - Article

AN - SCOPUS:85126792745

VL - 137

JO - Journal of Economic Dynamics and Control

JF - Journal of Economic Dynamics and Control

SN - 0165-1889

M1 - 104345

ER -

Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis

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Keywords

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