Research Article | OPEN ACCESS
Modeling the Implied Volatility Surface-: A Study for S&P 500 Index Option
1Jin Zheng and 2Yan Cai
1Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK
2Department of Mathematical Sciences, Xi’an Jiaotong University, Shanxi, Xi’an, 430079, China
Research Journal of Applied Sciences, Engineering and Technology 2013 6:1973-1977
Received: July 12, 2012 | Accepted: August 28, 2012 | Published: February 21, 2013
Abstract
The aim of this study is to demonstrate a framework to model the implied volatilities of S&P 500 index options and estimate the implied volatilities of stock prices using stochastic processes. In this paper, three models are established to estimate whether the implied volatilities are constant during the whole life of options. We mainly concentrate on the Black-Scholes and Dumas’ option models and make the empirical comparisons. By observing the daily-recorded data of S&P 500 index, we study the volatility model and volatility surface. Results from numerical experiments show that the stochastic volatilities are determined by moneyness rather than constant. Our research is of vital importance, especially for forecasting stock market shocks and crises, as one of the applications.
Keywords:
Moneyness, out-of-the money options, parameters estimation, volatility surface,
Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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