TITLE:
Estimation of Stochastic Volatility with a Compensated Poisson Jump Using Quadratic Variation
AUTHORS:
Perpetual Saah Andam, Joseph Ackora-Prah, Sure Mataramvura
KEYWORDS:
Stochastic Volatility, Compensated Poisson Jump, Quadratic Variation
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.7,
July
27,
2017
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.