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.
Highlights
Volatility is the downward and upward movements of the market
We present the estimation of stochastic volatility from the stochastic differential equation for evenly spaced data
We are motivated to propose a quadratic variation as a nonparametric method for estimating instantaneous volatility from a stochastic differential equation model by including compensated poisson jump as an extension
Summary
Volatility is the downward and upward movements of the market. Naturally stock prices attract volatility. Data available on prices of asset which are speculative allows quadratic variation method to be used to measure the activities of returns in financial market. We are motivated to propose a quadratic variation as a nonparametric method for estimating instantaneous volatility from a stochastic differential equation model by including compensated poisson jump as an extension. This jump process has an intensity which is able to capture the steepness and skewness in volatility smiles for short-dated options.
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