Higher order approximation of option prices in Barndorff-Nielsen and Shephard models

Álvaro Guinea Juliá and Alet Roux

Quantitative Finance, 2024, vol. 24, issue 8, 1057-1076

Abstract: We present an approximation method based on the mixing formula [Hull, J. and White, A., The pricing of options on assets with stochastic volatilities. J. Finance, 1987, 42, 281–300; Romano, M. and Touzi, N., Contingent claims and market completeness in a stochastic volatility model. Math. Finance, 1997, 7, 399–412] for pricing European options in Barndorff-Nielsen and Shephard models. This approximation is based on a Taylor expansion of the option price. It is implemented using a recursive algorithm that allows us to obtain closed form approximations of the option price of any order (subject to technical conditions on the background driving Lévy process). This method can be used for any type of Barndorff-Nielsen and Shephard stochastic volatility model. Explicit results are presented in the case where the stationary distribution of the background driving Lévy process is inverse Gaussian or gamma. In both of these cases, the approximation compares favorably to option prices produced by the characteristic function. In particular, we also perform an error analysis of the approximation, which is partially based on the results of Das and Langrené [Closed-form approximations with respect to the mixing solution for option pricing under stochastic volatility. Stochastics, 2022, 94, 745–788]. We obtain asymptotic results for the error of the $ N{{\rm th}} $ Nth order approximation and error bounds when the variance process satisfies an inverse Gaussian Ornstein–Uhlenbeck process or a gamma Ornstein–Uhlenbeck process.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/14697688.2024.2394220 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:24:y:2024:i:8:p:1057-1076

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RQUF20

DOI: 10.1080/14697688.2024.2394220

Access Statistics for this article

Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral

More articles in Quantitative Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().