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Simulation study on option pricing under jump diffusion models
Title
Simulation study on option pricing under jump diffusion models.
Creator
Rodrigues, Justin, Long, Hongwei, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
The main objective of this thesis is to simulate, evaluate and discuss several methods for pricing European-style options. The Black-Scholes model has long been considered the standard method for pricing options. One of the downfalls of the Black-Scholes model is that it is strictly continuous and does not incorporate discrete jumps. This thesis will consider two alternate Levy models that include discretized jumps; The Merton Jump Diffusion and Kou's Double Exponential Jump Diffusion. We...
Show moreThe main objective of this thesis is to simulate, evaluate and discuss several methods for pricing European-style options. The Black-Scholes model has long been considered the standard method for pricing options. One of the downfalls of the Black-Scholes model is that it is strictly continuous and does not incorporate discrete jumps. This thesis will consider two alternate Levy models that include discretized jumps; The Merton Jump Diffusion and Kou's Double Exponential Jump Diffusion. We will use each of the three models to price real world stock data through software simulations and explore the results.Keywords: Levy Processes, Brownian motion, Option pricing, Simulation, Black-Scholes, Merton Jump Diffusion, Kou, Kou's Double Exponential Jump Diffusion.
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Date Issued
2013
PURL
http://purl.flvc.org/fau/fd/FA0004051
Subject Headings
Finance -- Mathematical models, Levy processes, Prices -- Econometric models, Statistical physics, Stochastic processes, Valuation -- Econometric models
Format
Document (PDF)
Revisiting the methodology and application of Value-at-Risk
Title
Revisiting the methodology and application of Value-at-Risk.
Creator
Chung, Kyong., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
The main objective of this thesis is to simulate, evaluate and discuss three standard methodologies of calculating Value-at-Risk (VaR) : Historical simulation, the Variance-covariance method and Monte Carlo simulations. Historical simulation is the most common nonparametric method. The Variance-covariance and Monte Carlo simulations are widely used parametric methods. This thesis defines the three aforementioned VaR methodologies, and uses each to calculate 1-day VaR for a hypothetical...
Show moreThe main objective of this thesis is to simulate, evaluate and discuss three standard methodologies of calculating Value-at-Risk (VaR) : Historical simulation, the Variance-covariance method and Monte Carlo simulations. Historical simulation is the most common nonparametric method. The Variance-covariance and Monte Carlo simulations are widely used parametric methods. This thesis defines the three aforementioned VaR methodologies, and uses each to calculate 1-day VaR for a hypothetical portfolio through MATLAB simulations. The evaluation of the results shows that historical simulation yields the most reliable 1-day VaR for the hypothetical portfolio under extreme market conditions. Finally, this paper concludes with a suggestion for further studies : a heavy-tail distribution should be used in order to imporve the accuracy of the results for the two parametric methods used in this study.
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Date Issued
2012
PURL
http://purl.flvc.org/FAU/3358328
Subject Headings
Valuation, Econometric models, Prices, Econometric models, Financial risk management, Mathematical optimization, Finance, Mathematical models
Format
Document (PDF)