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Model-based pricing for financial derivatives

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  • Zhu, Ke
  • Ling, Shiqing
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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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 56623.

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Date of creation: 12 Jun 2014
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Handle: RePEc:pra:mprapa:56623

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Keywords: NGARCH; EGARCH and GJR models; Non-normal innovation; Option valuation; Risk neutralized measure; Volatility skew.;

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