Implied volatility from asian options via monte carlo methods

Zhaojun Yang; Christian Oliver Ewald; Yajun Xiao

doi:10.1142/S021902490900518X

Implied volatility from asian options via monte carlo methods

Zhaojun Yang^*
, Christian Oliver Ewald
, Yajun Xiao

^*Corresponding author for this work

Hunan University
University College Cork
University of St Andrews
Goethe University Frankfurt

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We discuss how implied volatilities for OTC traded Asian options can be computed by combining Monte Carlo techniques with the Newton method in order to solve nonlinear equations. The method relies on accurate and fast computation of the corresponding vegas of the option. In order to achieve this we propose the use of logarithmic derivatives instead of the classical approach. Our simulations document that the proposed method shows far better results than the classical approach. Furthermore we demonstrate how numerical results can be improved by localization.

Original language	English
Pages (from-to)	153-178
Number of pages	26
Journal	International Journal of Theoretical and Applied Finance
Volume	12
Issue number	2
DOIs	https://doi.org/10.1142/S021902490900518X
Publication status	Published - Mar 2009
Externally published	Yes

Keywords

Asian options
Calibration
Exotic options
Implied volatility
Local volatility
Monte Carlo simulation

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10.1142/S021902490900518X

Cite this

@article{85ce6c12398c465e8555f99962031401,

title = "Implied volatility from asian options via monte carlo methods",

abstract = "We discuss how implied volatilities for OTC traded Asian options can be computed by combining Monte Carlo techniques with the Newton method in order to solve nonlinear equations. The method relies on accurate and fast computation of the corresponding vegas of the option. In order to achieve this we propose the use of logarithmic derivatives instead of the classical approach. Our simulations document that the proposed method shows far better results than the classical approach. Furthermore we demonstrate how numerical results can be improved by localization.",

keywords = "Asian options, Calibration, Exotic options, Implied volatility, Local volatility, Monte Carlo simulation",

author = "Zhaojun Yang and Ewald, \{Christian Oliver\} and Yajun Xiao",

note = "Funding Information: The first author gratefully acknowledges grants from Chinese Social Science Fund (No. 06BJL022) and Natural Science Fund (No. 04JJ3009) of Hunan Province/China as well as support from the {\textquotedblleft}Economic Opening and Trade Development{\textquotedblright} project, Philosophy and Social Science Innovation Foundation of Hunan University 985 Engineering. The second author gratefully acknowledges support from the research grant {\textquotedblleft}Dependable adaptive systems and mathematical modeling{\textquotedblright}, Rheinland-Pfalz Excellence Cluster and DFG Grant 529817. Furthermore the second author would like to thank Ralf Korn and Olaf Menkens for many suggestions and fruitful discussions as well as an anonymous referee and the Managing Editor of IJTAF for many suggestions which helped to significantly improve the original article. The third author gratefully acknowledges a grant from the Graduate Program {\textquotedblright}Finance and Monetary Economics{\textquotedblright} of the Goethe University Frankfurt.",

year = "2009",

month = mar,

doi = "10.1142/S021902490900518X",

language = "English",

volume = "12",

pages = "153--178",

journal = "International Journal of Theoretical and Applied Finance",

issn = "0219-0249",

number = "2",

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TY - JOUR

T1 - Implied volatility from asian options via monte carlo methods

AU - Yang, Zhaojun

AU - Ewald, Christian Oliver

AU - Xiao, Yajun

N1 - Funding Information: The first author gratefully acknowledges grants from Chinese Social Science Fund (No. 06BJL022) and Natural Science Fund (No. 04JJ3009) of Hunan Province/China as well as support from the “Economic Opening and Trade Development” project, Philosophy and Social Science Innovation Foundation of Hunan University 985 Engineering. The second author gratefully acknowledges support from the research grant “Dependable adaptive systems and mathematical modeling”, Rheinland-Pfalz Excellence Cluster and DFG Grant 529817. Furthermore the second author would like to thank Ralf Korn and Olaf Menkens for many suggestions and fruitful discussions as well as an anonymous referee and the Managing Editor of IJTAF for many suggestions which helped to significantly improve the original article. The third author gratefully acknowledges a grant from the Graduate Program ”Finance and Monetary Economics” of the Goethe University Frankfurt.

PY - 2009/3

Y1 - 2009/3

N2 - We discuss how implied volatilities for OTC traded Asian options can be computed by combining Monte Carlo techniques with the Newton method in order to solve nonlinear equations. The method relies on accurate and fast computation of the corresponding vegas of the option. In order to achieve this we propose the use of logarithmic derivatives instead of the classical approach. Our simulations document that the proposed method shows far better results than the classical approach. Furthermore we demonstrate how numerical results can be improved by localization.

AB - We discuss how implied volatilities for OTC traded Asian options can be computed by combining Monte Carlo techniques with the Newton method in order to solve nonlinear equations. The method relies on accurate and fast computation of the corresponding vegas of the option. In order to achieve this we propose the use of logarithmic derivatives instead of the classical approach. Our simulations document that the proposed method shows far better results than the classical approach. Furthermore we demonstrate how numerical results can be improved by localization.

KW - Asian options

KW - Calibration

KW - Exotic options

KW - Implied volatility

KW - Local volatility

KW - Monte Carlo simulation

UR - https://www.scopus.com/pages/publications/67249148467

U2 - 10.1142/S021902490900518X

DO - 10.1142/S021902490900518X

M3 - Article

AN - SCOPUS:67249148467

SN - 0219-0249

VL - 12

SP - 153

EP - 178

JO - International Journal of Theoretical and Applied Finance

JF - International Journal of Theoretical and Applied Finance

IS - 2

ER -

Implied volatility from asian options via monte carlo methods

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Keywords

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