Asymptotic expansion for some local volatility models arising in finance

Sergio Albeverio (), Francesco Cordoni (), Luca Persio () and Gregorio Pellegrini ()
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Sergio Albeverio: University of Bonn
Francesco Cordoni: University of Verona
Luca Persio: University of Verona
Gregorio Pellegrini: Financial and Credit Risk, Gruppo Generali Italia Spa

Decisions in Economics and Finance, 2019, vol. 42, issue 2, No 9, 527-573

Abstract: Abstract In this paper, we study the small noise asymptotic expansions for certain classes of local volatility models arising in finance. We provide explicit expressions for the involved coefficients as well as accurate estimates on the remainders. Moreover, we perform a detailed numerical analysis, with accuracy comparisons, of the obtained results by means of the standard Monte Carlo technique as well as exploiting the Polynomial Chaos Expansion approach.

Keywords: Local volatility models; Small noise asymptotic expansions; Corrections to the Black–Scholes type models; Jump-diffusion models; Polynomial drift; Exponential drift; Polynomial Chaos Expansion method; Monte Carlo techniques (search for similar items in EconPapers)
JEL-codes: C02 C33 C63 C65 E43 E47 G11 G12 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10203-019-00247-w

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