Asymptotic expansion for some local volatility models arising in finance

被引：3

作者：

Albeverio, Sergio ^{[1
]}

Cordoni, Francesco ^{[2
]}

Di Persio, Luca ^{[2
]}

Pellegrini, Gregorio ^{[3
]}

机构：

[1] Univ Bonn, IZKS, BiBoS, HCM, Bonn, Germany

[2] Univ Verona, Dept Comp Sci, Str Grazie 15, Verona, Italy

[3] Grp Gen Italia Spa, Financial & Credit Risk, Trieste, Italy

来源：

DECISIONS IN ECONOMICS AND FINANCE | 2019年 / 42卷 / 02期

关键词：

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; MALLIAVIN CALCULUS; DRIVEN; NOISE; SDES;

D O I：

10.1007/s10203-019-00247-w

中图分类号：

O1 [数学]; C [社会科学总论];

学科分类号：

03 ; 0303 ; 0701 ; 070101 ;

摘要：

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.

引用

页码：527 / 573

页数：47

共 57 条

[1] A model with interacting assets driven by Poisson processes [J].