Explicit approximations of option prices via Malliavin calculus in a general stochastic volatility framework

Kaustav Das and Nicolas Langren\'e

Papers from arXiv.org

Abstract: We obtain an explicit approximation formula for European put option prices within a general stochastic volatility model with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula, reparameterising the volatility process and then performing a number of expansions. The bulk of the work is due to computing a number of expectations induced by the expansion procedure explicitly, which we achieve by appealing to techniques from Malliavin calculus. We obtain the explicit representation of the error generated by the expansion procedure, and bound it in terms of moments of functionals of the underlying volatility process. Under the assumption of piecewise-constant parameters, our approximation formulas become closed-form, and moreover we are able to establish a fast calibration scheme. Furthermore, we perform a numerical sensitivity analysis to investigate the quality of our approximation formula in the so-called Stochastic Verhulst model, and show that the errors are well within the acceptable range for application purposes.

Date: 2020-06, Revised 2025-01
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2006.01542 Latest version (application/pdf)

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:arx:papers:2006.01542

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators (help@arxiv.org).