Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 51 for “"Jump diffusion"”.
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Modelling Equities with a Stochastic Volatility Jump Diffusion
… examine the effects of stochastic volatility and jumps. Challenges surrounding application of this model are investigated through an evaluation of risk-neutral calibration and simulation methods. The model’s ability to fit the implied volatility surfaces from the JSE Top 40 equity index is …
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The dual jump diffusion model for security prices
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1993.
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Computational option pricing under jump diffusion and Lévy processes
The shortcomings of diffusion models in representing the risk related to large market movements have led to the development of various option pricing models with jumps. These models allow for a more realistic representation of price dynamics and greater flexibility in modelling and have therefore …
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Numerical Analysis of Jump-Diffusion Models for Option Pricing
Jump-diffusion models can under certain assumptions be expressed as partial integro-differential equations (PIDE). Such a PIDE typically involves a convection term and a nonlocal integral like for the here considered models of Merton and Kou. We transform the PIDE to eliminate the convection term, …
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Analysis of equity and interest rate returns in South Africa under the context of jump diffusion processes
… interest in the modelling of asset returns using jump diffusion processes. This was in part as a result of the realisation that the standard diffusion processes, which do not allow for jumps, were not able to capture the stylized facts that return distributions are leptokurtic and have heavy …
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Stability And Controls For Stochastic Dynamic Systems
… gives an in-depth study of stability of linear jump diffusion, linear Markovian jump diffusion, multi-dimensional jump diffusion and</p> <p>regime-switching jump diffusion together with the associated numerical solutions. The other part of our work is controls for stochastic dynamic systems, to …
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Modelling energy markets and pricing energy derivatives
… spot price behaviour, namely mean reversion and jumps. For the first time in the literature we test a jump diffusion model, and a mean reversion jump diffusion model against our broad data set and compare the findings to the Black's Geometric Brownian Motion specifications. In Chapter-4 we use a …
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Finite activity jump models for option pricing
… aims to look at option pricing under affine jump diffusion processes, with particular emphasis on using Fourier transforms. The focus of the thesis is on using Fourier transform to price European options and Barrier options under the Heston stochastic volatility model and the Bates model. …
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Option Pricing models with Stochastic Volatility and Jumps
… (such as stochastic volatility effects and jumps in the price of the underlying). This dissertation tackles the question of which option pricing model to use; it compares diffusion, pure jump and jump-diffusion models. All models are fitted to one-day price data on S&P500 European vanilla …
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Sampling error of the supremum of a Lévy process
… In particular, we discuss the cases of Merton's jump diffusion, compound Poisson with normal jumps, normal inverse Gaussian process, variance gamma process, Kou's jump diffusion and (symmetric) stable process. A general result on the upper bound estimate for the expected difference is also shown.
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Sensitivities in Option Pricing Models
… Black-Scholes model, the Heston's model and the jump diffusion model, for European type options. These adjoint equations can be used to compute the gradient of the cost function accurately for parameter estimation problems. The adjoint method allows efficient evaluation of the gradient of a cost …
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Analytical Estimation of Value at Risk Under Thick Tails and Fast Volatility Updating
… from stochastic volatility and event risk (jumps). Those two sources are not totally separated; under event risk, volatility updates faster than under normal market conditions. Generally, tail thickness is associated with hyper volatility updating. Existing VaR literature accounts partially …
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Efficient numerical methods based on integral transforms to solve option pricing problems
… then extend it to price options described by a jump-diffusion model, barrier options and the Heston’s volatility model. To approximate the integral part in the jump-diffusion model, we use the Gauss-Legendre quadrature method. Finally, we carry out extensive numerical simulations to value these …
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Essays on corporate bonds
… such as liquidity. I then calibrate a .jump diffusion model and a stochastic volatility model, finding that the jump diffusion model weakly improves cross-sectional explanatory power while the stochastic volatility model does not. However, much of the cross-sectional variation in yield …
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Forward and inverse American option pricing via a complementarity approach
… options under a local volatility model and two jump diffusion models: Kou's jump diffusion model and the Dupire system. In Chapter 2, we establish partial differential complementarity systems for pricing American options under the aforementioned three models. We also introduce two different …
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Error analysis of the COS method for options pricing
… CGMY, Normal Inverse Gaussian (NIG), Merton jump-diffusion, and Kou double-exponential jump model, which encompass a range of jump and heavy-tailed behaviors. Through extensive numerical experiments, we demonstrate that the COS method achieves high accuracy and rapid convergence across all …
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Modelling electricity price risk for the valuation of power contingent claims : the case of Nord Pool
… market; First, we propose a seasonal affine jump diffusion spike model, which can distinguish the behaviour of electricity spot prices between normal periods and periods when spikes occur. Second, we propose a seasonal affine jump diffusion regime-switching spike, which is an extension of the …
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Point symmetry methods for Itô Stochastic Differential Equations (SDE) with a finite jump process
… processes are the primary tools used in creating jump-diffusion process which is very popular in mathematical modeling. In financial mathematics, they are used to describe the change of stock rates and bonanzas, and they are often used in mathematical biology modeling and population dynamics. In …
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Hidden states, hidden structures: Bayesian learning in time series models
… system and parameter estimation in linear jump-diffusion systems, non-parametric model (system) estimation and batch audio restoration. For linear jump-diffusion systems, efficient state estimation methods based on the variable rate particle filter are presented for the general linear case …
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