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Showing 1 to 20 of 35 for “"stochastic volatility models"”.
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Pricing stochastic volatility models using random grids
… pricing under the Heston model as well as the stochastic local volatility model. Consistent results are obtained for a call option under the various pricing methods using similar parameters as those used in the random grids paper. More specifically, when using a Heston model, consistent prices …
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Pricing with Bivariate Unspanned Stochastic Volatility Models
Unspanned stochastic volatility (USV) models have gained popularity in the literature. USV models contain at least one source of volatility-related risk that cannot be hedged with bonds, referred to as the unspanned volatility factor(s). Bivariate USV models are the simplest case, comprising of one …
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Implementation of Bivariate Unspanned Stochastic Volatility Models
Unspanned stochastic volatility term structure models have gained popularity in the literature. This dissertation focuses on the challenges of implementing the simplest case – bivariate unspanned stochastic volatility models, where there is one state variable controlling the term structure, and one …
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Fractional stochastic volatility models: approximation, calibration and hedging
The area of modeling stochastic volatility using continuous time models has a long history and is always an interesting and vibrant area in financial mathematics, where the dynamic of the asset is a diffusion driven by Brownian motion and the dynamic of the volatility is associated with a diffusion …
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Stochastic Volatility Models for Contingent Claim Pricing and Hedging
… main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility curve. To achieve this we also propose that market volatility be modeled as random or stochastic …
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Estimating stochastic volatility models with student-t distributed errors
… the idea of Bollerslev (1987), estimating ARCH models with Student-t distributed errors, to estimating Stochastic Volatility (SV) models with Student-t distributed errors. It is unclear whether Gaussian distributed errors sufficiently account for the observed leptokurtosis in financial time …
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Asymptotics and numerics in rough and local stochastic volatility models
… from the modelling of asset prices. All these models have in common, that they permit the use of rough volatility processes, meaning that the fluctuations of stock prices are modelled via a very irregular process. Besides this underlying structure, statements about asymptotic behaviour play a …
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Extreme-Strike and Small-time Asymptotics for Gaussian Stochastic Volatility Models
<p>Asymptotic behavior of implied volatility is of our interest in this dissertation. For extreme strike, we consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting …
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Stochastic Volatility Models: Option Price Approximation, Asymptotics and Maximum Likelihood Estimation
… option pricing function and extract the latent volatility, thereby overcoming one of the key difficulties in the estimation problem. The method is applied to estimate three popular stochastic volatility models, two of which have not previously been amenable to maximum likelihood estimation with …
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Monte Carlo Methods for Derivative Pricing of Stochastic Volatility Models Driven by Fractional Brownian Motion
We model asset prices with stochastic volatilities driven by fractional Brownian motion. Price paths and their endpoints are used to obtain a Monte Carlo value estimate of vanilla european options, lookback options as well as variance swaps. Underlying models for price movements are driven by …
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Bayesian estimation of stochastic volatility models with fat tails and correlated errors applied to the South African financial market
… methods in the Bayesian framework to estimate Stochastic Volatility models using South African financial market data. A single move Gibbs sampler is used to sample parameters from the posterior distribution. Volatility is used as measure of an asset's risk. It is particularly important in risk …
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Long-memory stochastic volatility model calibration using deep neural nets
Widespread use of stochastic volatility models in the financial industry is bottlenecked by the complexity and intractability they present. Since the seminal work in quantitative finance by Black et al. and Merton, the infamous Black-Scholes model has been extensively used in the industry for …
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Option pricing with non-constant volatility
… past three decades, researchers have developed models to price options with non-constant asset price volatility. These models can be divided into deterministic volatility models and stochastic volatility models. Deterministic volatility models assume that volatility is determined by some …
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Local Stochastic Volatility—The Hyp-Hyp Model
Volatility modelling is used predominantly in order to explain the volatility smile observed in the market. Stochastic volatility models are mainly used to capture the curvature of a volatility smile while local volatility models generally model the skew. Jackel and Kahl ¨ (2008) present a …
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Essays on continuous time diffusion models.
… the past few decades, continuous time diffusion models have become an integral part of financial economics. Especially, in certain core areas in finance, such as interest rate, asset pricing, option pricing, portfolio selection and volatility modelling, continuous time diffusion models have …
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Rough volatility models
So-called rough stochastic volatility models constitute the latest advancement in option price modeling. In contrast to popular bivariate diffusion models such as Heston, here the driving noise of volatility is modeled by a fractional Brownian motion (fBM) with scaling in the rough regime of Hurst …
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A Study of Conditional Volatilities in Financial Markets using Generalized Conditional Heteroscedasticity Jump Models
… income and equities market using jump augmented stochastic volatility models. The results highlights that the fact that jumps are inherent in financial markets and have implications for the dynamics of volatilities and co-volatilities of financial assets over time. Jump augmented models provide a …
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Stochastic Volatility with Levy Processes: Calibration and Pricing
In this thesis, stochastic volatility models with Levy processes are treated in parameter calibration by the Carr-Madan fast Fourier transform (FFT) method and pricing through the partial integro-differential equation (PIDE) approach. First, different models where the underlying log stock price or …
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Essays on Measuring Monetary Policy Uncertainty and Forecasting Business Cycle
… can be applied to many flexible state space models such as non-linear, non-Gaussian, stochastic volatility models or stochastic volatility models with zero lower bound. These models have become increasingly popular in macro-economics and finance. The stochastic volatility model with zero …
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Malliavin Calculus in the Canonical Levy Process: White Noise Theory and Financial Applications.
… mean-variance hedging problem and applied it to stochastic volatility models such as the Barndorff-Nielsen and Shepard model model and the Bates model. A Donsker Delta approach is employed on a Binary option to solve the mean-variance hedging problem. Finally, we are able to derive the Delta and …
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