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Approximating stochastic volatility by recombinant trees
American options stochastic volatility Heston model correlated random walk
2012/6/5
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting...
Maximum likelihood approach for several stochastic volatility models
Maximum likelihood approach several stochastic volatility models Computational Finance
2012/4/28
Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method...
Realized Wavelet Jump-GARCH model: Can wavelet decomposition of volatility improve its forecasting?
wavelet decomposition jumps volatility forecasting Realized GARCH
2012/4/28
In this paper, we propose a forecasting model for volatility based on its decomposition to several investment horizons and jumps. As a forecasting tool, we utilize Realized GARCH framework of Hansen e...
Bayesian Inference of Stochastic Volatility Model by Hybrid Monte Carlo
Hybrid Monte Carlo Algorithm Stochastic Volatility Model
2010/10/18
The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility va...
A remark on Gatheral's 'most-likely path approximation' of implied volatility
remark on Gatheral's 'most-likely path implied volatility
2010/11/2
We give a rigorous proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we fix the problem of a circular defi...
Nonparametric methods for volatility density estimation
stochastic volatility models deconvolution density estimation kernel estimator wavelets minimum contrast estimation
2010/11/2
Stochastic volatility modelling of nancial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparam...
Most Efficient Homogeneous Volatility Estimators
Variance and volatility estimators efficiency homogeneous functions Variance and volatility estimators efficiency homogeneous functions
2010/11/2
We present a new theory of homogeneous volatility (and variance) estimators for arbitrary stochastic processes. The main tool of our theory is the parsimonious encoding of all the information containe...
Regime Switching Stochastic Volatility with Perturbation Based Option Pricing
Stochastic volatility option pricing perturbation theory
2010/10/29
Volatility modelling has become a significant area of research within Financial Mathematics. Wiener process driven stochastic volatility models have become popular due their consistency with theoretic...
Solvable Nonlinear Volatility Diffusion Models with Affine Drift
Solvable Nonlinear Volatility Diffusion Models Affine Drift
2010/11/1
We present a method for constructing new families of solvable one-dimensional di usions with linear drift and nonlinear di usion coecient functions, whose tran-sition densities are obtainable in anal...
Asymptotic Implied Volatility at the Second Order with Application to the SABR Model
Stochastic volatility Asymptotic expansion Heat kernel
2010/11/1
We provide a general method to compute a Taylor expansion in time of implied volatility for
stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is...
Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes
Call and put pricing functions Implied volatility Asymptotic formulas Pareto-type distributions Regularly varying functions
2010/11/1
In this paper, we obtain asymptotic formulas with error estimates for the implied volatility
associated with a European call pricing function. We show that these formulas imply Lee’s moment formulas ...