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Estimation of Stochastic Volatility with a Compensated Poisson Jump Using Quadratic Variation
Department of Mathematics, Kwame Nkrumah University of Science and Technology (KNUST), Kumasi, Ghana
Department of Mathematics, Kwame Nkrumah University of Science and Technology (KNUST), Kumasi, Ghana
Department of Actuarial Science, University of Cape Town, Cape Town, South Africa
- 1 Department of Mathematics, Kwame Nkrumah University of Science and Technology (KNUST), Kumasi, Ghana
- 2 Department of Mathematics, Kwame Nkrumah University of Science and Technology (KNUST), Kumasi, Ghana
- 3 Department of Actuarial Science, University of Cape Town, Cape Town, South Africa
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Abstract
The degree of variation of trading prices with respect to time is volatility-measured by the standard deviation of returns. We present the estimation of stochastic volatility from the stochastic differential equation for evenly spaced data. We indicate that, the price process is driven by a semi-martingale and the data are evenly spaced. The results of Malliavin and Mancino [1] are extended by adding a compensated poisson jump that uses a quadratic variation to calculate volatility. The volatility is computed from a daily data without assuming its functional form. Our result is well suited for financial market applications and in particular the analysis of high frequency data for the computation of volatility.
KeywordsStochastic VolatilityCompensated Poisson JumpQuadratic Variation
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