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Model-based pricing for financial derivatives
Zhu, Ke1; Ling, Shiqing2
AbstractAssume that S-t is a stock price process and B-t is a bond price process with a constant continuously compounded risk-free interest rate, where both are defined on an appropriate probability space P. Let y(t) = log(S-t/St-1). yt can be generally decomposed into a conditional mean plus a noise with volatility components, but the discounted S-t is not a martingale under P. Under a general framework, we obtain a risk-neutralized measure Q under which the discounted St is a martingale in this paper. Using this measure, we show how to derive the risk neutralized price for the derivatives. Special examples, such as NGARCH, EGARCH and GJR pricing models, are given. Simulation study reveals that these pricing models can capture the "volatility skew" of implied volatilities in the European option. A small application highlights the importance of our model-based pricing procedure. (C) 2015 Elsevier B.V. All rights reserved.
KeywordNGARCH EGARCH and GJR models Non-normal innovation Option valuation Risk neutralized measure Volatility skew
Funding ProjectHong Kong Research Grants Commission[HKUST641912] ; Hong Kong Research Grants Commission[HKUST603413] ; National Natural Science Foundation of China[11201459] ; National Natural Science Foundation of China[11371354] ; Chinese Academy of Sciences[2014-cjrwlzx-zk] ; Key Laboratory of RCSDS ; President Fund of the Academy of Mathematics and System Science
WOS Research AreaBusiness & Economics ; Mathematics ; Mathematical Methods In Social Sciences
WOS SubjectEconomics ; Mathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods
WOS IDWOS:000357348300005
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Document Type期刊论文
Corresponding AuthorLing, Shiqing
Affiliation1.Chinese Acad Sci, Inst Appl Math, Beijing, Peoples R China
2.Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China
Recommended Citation
GB/T 7714
Zhu, Ke,Ling, Shiqing. Model-based pricing for financial derivatives[J]. JOURNAL OF ECONOMETRICS,2015,187(2):447-457.
APA Zhu, Ke,&Ling, Shiqing.(2015).Model-based pricing for financial derivatives.JOURNAL OF ECONOMETRICS,187(2),447-457.
MLA Zhu, Ke,et al."Model-based pricing for financial derivatives".JOURNAL OF ECONOMETRICS 187.2(2015):447-457.
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