COMPUTATION OF VOLATILITY IN STOCHASTIC VOLATILITY MODELS WITH HIGH FREQUENCY DATA

2010 ◽  
Vol 13 (05) ◽  
pp. 767-787 ◽  
Author(s):  
EMILIO BARUCCI ◽  
MARIA ELVIRA MANCINO
Keyword(s):  
Stochastic Volatility ◽  
High Frequency ◽  
Asset Price ◽  
Heston Model ◽  
High Frequency Data ◽  
Monte Carlo Experiment ◽  
Price Model ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Correlation Parameters

We consider general stochastic volatility models driven by continuous Brownian semimartingales, we show that the volatility of the variance and the leverage component (covariance between the asset price and the variance) can be reconstructed pathwise by exploiting Fourier analysis from the observation of the asset price. Specifying parametrically the asset price model we show that the method allows us to compute the parameters of the model. We provide a Monte Carlo experiment to recover the volatility and correlation parameters of the Heston model.

scholarly journals FAST HILBERT TRANSFORM ALGORITHMS FOR PRICING DISCRETE TIMER OPTIONS UNDER STOCHASTIC VOLATILITY MODELS

2015 ◽  
Vol 18 (07) ◽  
pp. 1550046 ◽  
Author(s):  
PINGPING ZENG ◽  
YUE KUEN KWOK ◽  
WENDONG ZHENG
Keyword(s):  
Stochastic Volatility ◽  
Hilbert Transform ◽  
Asset Price ◽  
Heston Model ◽  
Expiration Date ◽  
Realized Variance ◽  
Stochastic Volatility Models ◽  
Underlying Asset ◽  
Volatility Models ◽  
Volatility Model

Timer options are barrier style options in the volatility space. A typical timer option is similar to its European vanilla counterpart, except with uncertain expiration date. The finite-maturity timer option expires either when the accumulated realized variance of the underlying asset has reached a pre-specified level or on the mandated expiration date, whichever comes earlier. The challenge in the pricing procedure is the incorporation of the barrier feature in terms of the accumulated realized variance instead of the usual knock-out feature of hitting a barrier by the underlying asset price. We construct the fast Hilbert transform algorithms for pricing finite-maturity discrete timer options under different types of stochastic volatility processes. The stochastic volatility processes nest some popular stochastic volatility models, like the Heston model and 3/2 stochastic volatility model. The barrier feature associated with the accumulated realized variance can be incorporated effectively into the fast Hilbert transform procedure with the computational convenience of avoiding the nuisance of recovering the option values in the real domain at each monitoring time instant in order to check for the expiry condition. Our numerical tests demonstrate high level of accuracy of the fast Hilbert transform algorithms. We also explore the pricing properties of the timer options with respect to various parameters, like the volatility of variance, correlation coefficient between the asset price process and instantaneous variance process, sampling frequency, and variance budget.

scholarly journals INTEGRAL REPRESENTATION OF PROBABILITY DENSITY OF STOCHASTIC VOLATILITY MODELS AND TIMER OPTIONS

2017 ◽  
Vol 20 (08) ◽  
pp. 1750055 ◽  
Author(s):  
ZHENYU CUI ◽  
J. LARS KIRKBY ◽  
GUANGHUA LIAN ◽  
DUY NGUYEN
Keyword(s):  
Stochastic Volatility ◽  
Probabilistic Method ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Model Parameters ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Probability Densities ◽  
Special Case

This paper contributes a generic probabilistic method to derive explicit exact probability densities for stochastic volatility models. Our method is based on a novel application of the exponential measure change in [Z. Palmowski & T. Rolski (2002) A technique for exponential change of measure for Markov processes, Bernoulli 8(6), 767–785]. With this generic approach, we first derive explicit probability densities in terms of model parameters for several stochastic volatility models with nonzero correlations, namely the Heston 1993, [Formula: see text], and a special case of the [Formula: see text]-Hypergeometric stochastic volatility models recently proposed by [J. Da Fonseca & C. Martini (2016) The [Formula: see text]-Hypergeometric stochastic volatility model, Stochastic Processes and their Applications 126(5), 1472–1502]. Then, we combine our method with a stochastic time change technique to develop explicit formulae for prices of timer options in the Heston model, the [Formula: see text] model and a special case of the [Formula: see text]-Hypergeometric model.

A comparison of option pricing models

2017 ◽  
Vol 04 (02n03) ◽  
pp. 1750024
Author(s):  
Elham Dastranj ◽  
Roghaye Latifi
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Heston Model ◽  
Pricing Models ◽  
Stochastic Volatility Models ◽  
Numerical Examples ◽  
Call Options ◽  
Volatility Models ◽  
Premium Income

Option pricing under two stochastic volatility models, double Heston model and double Heston with three jumps, is done. Firstly, the efficiency of the second model is shown via FFT method, and numerical examples using power call options. Then it is shown that power option yields more premium income under the second model, double Heston with three jumps, than another one.

Long-Time Trajectorial Large Deviations and Importance Sampling for Affine Stochastic Volatility Models

2021 ◽  
Vol 53 (1) ◽  
pp. 220-250
Author(s):  
Zorana Grbac ◽  
David Krief ◽  
Peter Tankov
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
Variance Reduction ◽  
Large Deviation ◽  
Heston Model ◽  
Stochastic Volatility Models ◽  
Monte Carlo Computation ◽  
Volatility Models ◽  
Long Time ◽  
Path Dependent

AbstractWe establish a pathwise large deviation principle for affine stochastic volatility models introduced by Keller-Ressel (2011), and present an application to variance reduction for Monte Carlo computation of prices of path-dependent options in these models, extending the method developed by Genin and Tankov (2020) for exponential Lévy models. To this end, we apply an exponentially affine change of measure and use Varadhan’s lemma, in the fashion of Guasoni and Robertson (2008) and Robertson (2010), to approximate the problem of finding the measure that minimizes the variance of the Monte Carlo estimator. We test the method on the Heston model with and without jumps to demonstrate its numerical efficiency.

scholarly journals FRACTIONAL COINTEGRATION IN STOCHASTIC VOLATILITY MODELS

2008 ◽  
Vol 24 (5) ◽  
pp. 1207-1253 ◽  
Author(s):  
Afonso Gonçalves da Silva ◽  
Peter M. Robinson
Keyword(s):  
Stochastic Volatility ◽  
Latent Variables ◽  
Factor Model ◽  
Strong Dependence ◽  
Common Factor ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Finite Sample Properties

Asset returns are frequently assumed to be determined by one or more common factors. We consider a bivariate factor model where the unobservable common factor and idiosyncratic errors are stationary and serially uncorrelated but have strong dependence in higher moments. Stochastic volatility models for the latent variables are employed, in view of their direct application to asset pricing models. Assuming that the underlying persistence is higher in the factor than in the errors, a fractional cointegrating relationship can be recovered by suitable transformation of the data. We propose a narrow band semiparametric estimate of the factor loadings, which is shown to be consistent with a rate of convergence, and its finite-sample properties are investigated in a Monte Carlo experiment.

scholarly journals A Estimation of Stochastic Volatility Models Using Optimized Filtering Algorithms

2019 ◽  
Vol 48 (2) ◽  
Author(s):  
Saba Infante ◽  
Cesar Luna ◽  
Luis Sanchez ◽  
Aracelis Hernández
Keyword(s):  
Particle Filter ◽  
Stochastic Volatility ◽  
Viterbi Algorithm ◽  
Joint Estimation ◽  
Heston Model ◽  
Parameter Estimates ◽  
Stochastic Volatility Models ◽  
Filtering Algorithms ◽  
Volatility Models ◽  
Computational Calculations

In this paper, we describe and implement two recursive filtering algorithms, the optimized particle filter, and the Viterbi algorithm, which allow the joint estimation of states and parameters of continuous-time stochastic volatility models, such as the Cox Ingersoll Ross and Heston model. In practice, good parameter estimates are required so that the models are able to generate accurate forecasts. To achieve the objectives the proposed algorithms were implemented using daily empirical data from the time series of the $S\&P500$ returns of the stock exchange index. The proposed methodology facilitates computational calculations of the marginal likelihood of states and allows the reconstruction of unknown states in a suitable way, and reliable estimation of the parameters. To measure the quality of estimation of the algorithms, we used the square root of the mean square error and relative deviation standard as measures of goodness of fit. The estimated errors are insignificant for the analyzed data and the two models considered. We also calculated the execution times of the algorithms, demonstrating that the Viterbi algorithm has less execution time than the optimized particle filter.

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