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Model-based pricing for financial derivatives

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  • Zhu, Ke
  • Ling, Shiqing

Abstract

Assume that S_{t} is a stock price process and Bt 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}/S_{t-1}). y_{t} can be generally decomposed into a conditional mean plus a noise with volatility components, but the discounted St 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.

Suggested Citation

  • Zhu, Ke & Ling, Shiqing, 2014. "Model-based pricing for financial derivatives," MPRA Paper 56623, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:56623
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    Cited by:

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    2. Donghang Luo & Ke Zhu & Huan Gong & Dong Li, 2020. "Testing error distribution by kernelized Stein discrepancy in multivariate time series models," Papers 2008.00747, arXiv.org.
    3. Chang, Chia-Lin & McAleer, Michael, 2015. "Econometric analysis of financial derivatives: An overview," Journal of Econometrics, Elsevier, vol. 187(2), pages 403-407.
    4. Chang, C-L. & McAleer, M.J., 2014. "Econometric Analysis of Financial Derivatives," Econometric Institute Research Papers EI 2015-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Zhu, Ke, 2015. "Hausman tests for the error distribution in conditionally heteroskedastic models," MPRA Paper 66991, University Library of Munich, Germany.
    6. Jiawen Luo & Oguzhan Cepni & Riza Demirer & Rangan Gupta, 2022. "Forecasting Multivariate Volatilities with Exogenous Predictors: An Application to Industry Diversification Strategies," Working Papers 202258, University of Pretoria, Department of Economics.

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    More about this item

    Keywords

    NGARCH; EGARCH and GJR models; Non-normal innovation; Option valuation; Risk neutralized measure; Volatility skew.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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