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Extra-Dimensional Approach to Option Pricing and Stochastic Volatility
Extra-Dimensional Option Pricing Stochastic Volatility
2010/10/18
The generalized 5D Black-Scholes differential equation with stochastic volatility is derived. The projections of the stochastic evolutions associated with the random variables from an enlarged space o...
Is the minimum value of an option on variance generated by local volatility?
minimum value option local volatility
2010/10/18
We discuss the possibility of obtaining model-free bounds on volatility derivatives, given present market data in the form of a calibrated local volatility model. A counter-example to a wide-spread co...
Option pricing in multivariate stochastic volatility models of OU type
multivariate stochastic volatility models Ornstein-Uhlenbeck type processes option pricing
2010/10/18
We present a multivariate stochastic volatility model with leverage, which is flexible enough to recapture the individual dynamics as well as the interdependencies between several assets while still ...
On refined volatility smile expansion in the Heston model
refined volatility expansion Heston model
2010/10/18
It is known that Heston's stochastic volatility model exhibits moment explosion, and that the critical moment $s^{*}$ can be obtained by solving (numerically) a simple equation. This yields a leading ...
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...
Finite-size effect and the components of multifractality in financial volatility
Finite-size effect components of multifractality financial volatility
2010/11/3
Many financial variables are found to exhibit multifractal nature, which is usually attributed
to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF).Based...
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...
On the Value–Volatility Relationship in a Real Options Model
investment analysis option-pricing theory finance nonlinear stochastic differential equation
2009/5/7
In the analytical real options approach, the most important proposition that the value of the investment opportunity increases as the volatility increases has been proved by assuming the convexity of...
First-passage and risk evaluation under stochastic volatility
First-passage risk evaluation
2010/10/29
We solve the first-passage problem for the Heston random diffusion model. We obtain exact
analytical expressions for the survival and hitting probabilities to a given level of return. We study severa...
Volatility forecasts and the at-the-money implied volatility: a multi-components ARCH approach and its relation with market models
Volatility forecasts at-the-money implied relation
2010/10/29
For a given time horizon T, this article explores the relationship between the realized volatility (the volatility that will occur between t and t + T), the implied volatility (corresponding to at-t...
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...
Regime Switching Volatility Calibration by the Baum-Welch Method
Regime switching stochastic volatility calibration Hamilton filter Baum-Welch
2010/10/29
Regime switching volatility models provide a tractable method of modelling stochastic volatility. Currently the most popular method of regime switching calibration is the Hamilton filter. We propose u...