179 research outputs found
Monte Carlo simulation for Barndorff-Nielsen and Shephard model under change of measure
The Barndorff-Nielsen and Shephard model is a representative jump-type
stochastic volatility model. Still, no method exists to compute option prices
numerically for the non-martingale case with infinite active jumps. We develop
two simulation methods for such a case under change of measure and conduct some
numerical experiments
Pricing Nikkei 225 Options Using Realized Volatility
This article analyzes whether daily realized volatility, which is the sum of squared intraday returns over a day, is useful for option pricing. Different realized volatilities are calculated with or without taking account of microstructure noise and with or without using overnight and lunch-time returns. ARFIMA, ARFIMAX, HAR, HARX models are employed to specify the dynamics of realized volatility. ARFIMA and HAR models can capture the long-memory property and ARFIMAX and HARX models can also capture the asymmetry in volatility depending on the sign of previous day's return. Option prices are derived under the assumption of risk-neutrality. For comparison, GARCH, EGARCH and FIEGARCH models are estimated using daily returns, where option prices are derived by assuming the risk-neutrality and by using the Duan (1995) method in which the assumption of risk-neutrality is relaxed. Main results using the Nikkei 225 stock index and its put options prices are: (1) ARFIMAX model with daily realized volatility performs best, (2) the Hansen and Lunde ( 2005a) adjustment without using overnight and lunch-time returns can improve the performance, (3) if the Hansen and Lunde (2005a), which also plays a role to remove the bias caused by the microstructure noise by setting the sample mean of realized volatility equal to the sample variance of daily returns, is used, the other methods for taking account of microstructure noise do not necessarily improve the performance and (4) the Duan (1995) method does not improve the performance compared with assuming the risk neutrality.microstructure noise, Nikkei 225 stock index, non-trading hours, option pricing, realized volatility
Stochastic volatility modeling of high-frequency CSI 300 index and dynamic jump prediction driven by machine learning
This paper models stochastic process of price time series of CSI 300 index in
Chinese financial market, analyzes volatility characteristics of intraday
high-frequency price data. In the new generalized Barndorff-Nielsen and
Shephard model, the lag caused by asynchrony of market information is
considered, and the problem of lack of long-term dependence is solved. To speed
up the valuation process, several machine learning and deep learning algorithms
are used to estimate parameter and evaluate forecast results. Tracking
historical jumps of different magnitudes offers promising avenues for
simulating dynamic price processes and predicting future jumps. Numerical
results show that the deterministic component of stochastic volatility
processes would always be captured over short and longer-term windows. Research
finding could be suitable for influence investors and regulators interested in
predicting market dynamics based on realized volatility
Nonparametric estimation for Levy processes with a view towards mathematical finance
Nonparametric methods for the estimation of the Levy density of a Levy
process are developed. Estimators that can be written in terms of the ``jumps''
of the process are introduced, and so are discrete-data based approximations. A
model selection approach made up of two steps is investigated. The first step
consists in the selection of a good estimator from a linear model of proposed
Levy densities, while the second is a data-driven selection of a linear model
among a given collection of linear models. By providing lower bounds for the
minimax risk of estimation over Besov Levy densities, our estimators are shown
to achieve the ``best'' rate of convergence. A numerical study for the case of
histogram estimators and for variance Gamma processes, models of key importance
in risky asset price modeling driven by Levy processes, is presented.Comment: 68 pages, 19 figures, submitted to Annals of Statistic
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