VOLATILITY SMILE INTERPOLATION WITH RADIAL BASIS FUNCTIONS

被引：0

作者：

Donfack, Hermann Azemtsa ^{[1
]}

Soh, Celestin Wafo ^{[1
,2
]}

Kotze, Antonie ^{[1
]}

机构：

[1] Univ Johannesburg, Dept Finance & Investment Management, Johannesburg, Gauteng, South Africa

[2] Jackson State Univ, Coll Sci Engn & Technol, Dept Math & Stat Sci, Jackson, MS 39217 USA

来源：

INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE | 2022年 / 25卷 / 7-8期

关键词：

RBF; radial basis function; volatility; risk-neutral density; local volatility; BENCHMARKING PROJECT; SURFACES; BENCHOP;

D O I：

10.1142/S0219024922500303

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

摘要：

The Radial Basis Functions (RBF) interpolation is a popular approximation technique used to smooth scattered data in various dimensions. This study uses RBF interpolation to interpolate the volatility skew of the S & P500 index options. The interpolated skews are used to construct the risk-neutral densities of the index and its local volatility surface. The RBF interpolation is contrasted throughout the study with the cubic spline interpolation. An analysis of the densities and the local volatility shows that RBF are an effective and practical tool for interpolating the implied volatility surface.

引用

页数：23

共 34 条

[1]

[Anonymous], 2005, Volatility and correlation: The perfect hedger and the fox

[2]

Bergomi Lorenzo, 2015, Stochastic volatility modeling

[3]

Bossu S, 2014, Advanced equity derivatives: Volatility and correlation

[4] PRICES OF STATE-CONTINGENT CLAIMS IMPLICIT IN OPTION PRICES [J].

BREEDEN, DT ;

LITZENBERGER, RH .

JOURNAL OF BUSINESS, 1978, 51 (04) :621-651

[5] Deep Local Volatility [J].

Chataigner, Marc ;

Crepey, Stephane ;

Dixon, Matthew .

RISKS, 2020, 8 (03) :1-18

[6] Direct solution of Navier-Stokes equations by radial basis functions [J].

Demirkaya, G. ;

Soh, C. Wafo ;

Ilegbusi, O. J. .

APPLIED MATHEMATICAL MODELLING, 2008, 32 (09) :1848-1858

[7]

Derman E., 1994, GOLDMAN SACHS QUANT, V2, P45

[8] Implied volatility functions: Empirical tests [J].

Dumas, B ;

Fleming, J ;

Whaley, RE .

JOURNAL OF FINANCE, 1998, 53 (06) :2059-2106

[9]

Dupire B., 1994, RISK, V7, P18

[10] On choosing "optimal" shape parameters for RBF approximation [J].

Fasshatier, Gregory E. ;

Zhang, Jack G. .

NUMERICAL ALGORITHMS, 2007, 45 (1-4) :345-368

← 1 2 3 4 →