Dissertations / Theses on the topic 'Jump Diffusion Model'
To see the other types of publications on this topic, follow the link: Jump Diffusion Model.
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Jump Diffusion Model.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Frost, Daniel Allen. "The dual jump diffusion model for security prices." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/12509.
Full textAbstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1993.Vita.
Includes bibliographical references (leaves 225-227).
by Daniel Allen Frost.
Ph.D.
2
Berros, Jeremy. "American option pricing in a jump-diffusion model." [Gainesville, Fla.] : University of Florida, 2009. http://purl.fcla.edu/fcla/etd/UFE0025116.
Full text
3
Tang, Furui. "Merton Jump-Diffusion Modeling of Stock Price Data." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-78351.
Full textAbstract:
In this thesis, we investigate two stock price models, the Black-Scholes (BS) model and the Merton Jump-Diffusion (MJD) model. Comparing the logarithmic return of the BS model and the MJD model with empirical stock price data, we conclude that the Merton Jump-Diffusion Model is substantially more suitable for the stock market. This is concluded visually not only by comparing the density functions but also by analyzing mean, variance, skewness and kurtosis of the log-returns. One technical contribution to the thesis is a suggested decision rule for initial guess of a maximum likelihood estimation of the MJD-modeled parameters.
4
Nassar, Hiba. "Regularized Calibration of Jump-Diffusion Option Pricing Models." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-9063.
Full textAbstract:
An important issue in finance is model calibration. The calibration problem is the inverse of the option pricing problem. Calibration is performed on a set of option prices generated from a given exponential L´evy model. By numerical examples, it is shown that the usual formulation of the inverse problem via Non-linear Least Squares is an ill-posed problem. To achieve well-posedness of the problem, some regularization is needed. Therefore a regularization method based on relative entropy is applied.
5
Bu, Tianren. "Option pricing under exponential jump diffusion processes." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/option-pricing-under-exponential-jump-diffusion-processes(0dab0630-b8f8-4ee8-8bf0-8cd0b9b9afc0).html.
Full textAbstract:
The main contribution of this thesis is to derive the properties and present a closed from solution of the exotic options under some specific types of Levy processes, such as American put options, American call options, British put options, British call options and American knock-out put options under either double exponential jump-diffusion processes or one-sided exponential jump-diffusion processes. Compared to the geometric Brownian motion, exponential jump-diffusion processes can better incorporate the asymmetric leptokurtic features and the volatility smile observed from the market. Pricing the option with early exercise feature is the optimal stopping problem to determine the optimal stopping time to maximize the expected options payoff. Due to the Markovian structure of the underlying process, the optimal stopping problem is related to the free-boundary problem consisting of an integral differential equation and suitable boundary conditions. By the local time-space formula for semi-martingales, the closed form solution for the options value can be derived from the free-boundary problem and we characterize the optimal stopping boundary as the unique solution to a nonlinear integral equation arising from the early exercise premium (EEP) representation. Chapter 2 and Chapter 3 discuss American put options and American call options respectively. When pricing options with early exercise feature under the double exponential jump-diffusion processes, a non-local integral term will be found in the infinitesimal generator of the underlying process. By the local time-space formula for semi-martingales, we show that the value function and the optimal stopping boundary are the unique solution pair to the system of two integral equations. The significant contributions of these two chapters are to prove the uniqueness of the value function and the optimal stopping boundary under less restrictive assumptions compared to previous literatures. In the degenerate case with only one-sided jumps, we find that the results are in line with the geometric Brownian motion models, which extends the analytical tractability of the Black-Scholes analysis to alternative models with jumps. In Chapter 4 and Chapter 5, we examine the British payoff mechanism under one-sided exponential jump-diffusion processes, which is the first analysis of British options for process with jumps. We show that the optimal stopping boundaries of British put options with only negative jumps or British call options with only positive jumps can also be characterized as the unique solution to a nonlinear integral equation arising from the early exercise premium representation. Chapter 6 provides the study of American knock-out put options under negative exponential jump-diffusion processes. The conditional memoryless property of the exponential distribution enables us to obtain an analytical form of the arbitrage-free price for American knock-out put options, which is usually more difficult for many other jump-diffusion models.
6
Düvelmeyer, Dana. "Some stability results of parameter identification in a jump diffusion model." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501234.
Full textAbstract:
In this paper we discuss the stable solvability of the inverse problem of parameter identification in a jump diffusion model. Therefore we introduce the forward
operator of this inverse problem and analyze its properties. We show continuity of
the forward operator and stability of the inverse problem provided that the domain
is restricted in a specific manner such that techniques of compact sets can be exploited. Furthermore, we show that there is an asymptotical non-injectivity which
causes instability problems whenever the jump intensity increases and the jump
heights decay simultaneously.
7
Starkloff, Hans-Jörg, Dana Düvelmeyer, and Bernd Hofmann. "A note on uniqueness of parameter identification in a jump diffusion model." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501325.
Full textAbstract:
In this note, we consider an inverse problem in a jump diffusion model. Using
characteristic functions we prove the injectivity of the forward operator mapping
the five parameters determining the model to the density function of the return
distribution.
8
Chen, Hongqing. "An Empirical Study on the Jump-diffusion Two-beta Asset Pricing Model." PDXScholar, 1996. https://pdxscholar.library.pdx.edu/open_access_etds/1325.
Full textAbstract:
This dissertation focuses on testing and exploring the usage of the jump-diffusion two-beta asset pricing model. Daily and monthly security returns from both NYSE and AMEX are employed to form various samples for the empirical study. The maximum likelihood estimation is employed to estimate parameters of the jump-diffusion processes. A thorough study on the existence of jump-diffusion processes is carried out with the likelihood ratio test. The probability of existence of the jump process is introduced as an indicator of "switching" between the diffusion process and the jump process. This new empirical method marks a contribution to future studies on the jump-diffusion process. It also makes the jump-diffusion two-beta asset pricing model operational for financial analyses. Hypothesis tests focus on the specifications of the new model as well as the distinction between it and the conventional capital asset pricing model. Both parametric and non-parametric tests are carried out in this study. Comparing with previous models on the risk-return relationship, such as the capital asset pricing model, the arbitrage pricing theory and various multi-factor models, the jump-diffusion two-beta asset pricing model is simple and intuitive. It possesses more explanatory power when the jump process is dominant. This characteristic makes it a better model in explaining the January effect. Extra effort is put in the study of the January Effect due to the importance of the phenomenon. Empirical findings from this study agree with the model in that the systematic risk of an asset is the weighted average of both jump and diffusion betas. It is also found that the systematic risk of the conventional CAPM does not equal the weighted average of jump and diffusion betas.
9
Lee, Brendan Chee-Seng Banking & Finance Australian School of Business UNSW. "Incorporating discontinuities in value-at-risk via the poisson jump diffusion model and variance gamma model." Awarded by:University of New South Wales, 2007. http://handle.unsw.edu.au/1959.4/37201.
Full textAbstract:
We utilise several asset pricing models that allow for discontinuities in the returns and volatility time series in order to obtain estimates of Value-at-Risk (VaR). The first class of model that we use mixes a continuous diffusion process with discrete jumps at random points in time (Poisson Jump Diffusion Model). We also apply a purely discontinuous model that does not contain any continuous component at all in the underlying distribution (Variance Gamma Model). These models have been shown to have some success in capturing certain characteristics of return distributions, a few being leptokurtosis and skewness. Calibrating these models onto the returns of an index of Australian stocks (All Ordinaries Index), we then use the resulting parameters to obtain daily estimates of VaR. In order to obtain the VaR estimates for the Poisson Jump Diffusion Model and the Variance Gamma Model, we introduce the use of an innovation from option pricing techniques, which concentrates on the more tractable characteristic functions of the models. Having then obtained a series of VaR estimates, we then apply a variety of criteria to assess how each model performs and also evaluate these models against the traditional approaches to calculating VaR, such as that suggested by J.P. Morgan???s RiskMetrics. Our results show that whilst the Poisson Jump Diffusion model proved the most accurate at the 95% VaR level, neither the Poisson Jump Diffusion or Variance Gamma models were dominant in the other performance criteria examined. Overall, no model was clearly superior according to all the performance criteria analysed, and it seems that the extra computational time required to calibrate the Poisson Jump Diffusion and Variance Gamma models for the purposes of VaR estimation do not provide sufficient reward for the additional effort than that currently employed by Riskmetrics.
10
Reducha, Wojciech. "Parameter Estimation of the Pareto-Beta Jump-Diffusion Model in Times of Catastrophe Crisis." Thesis, Högskolan i Halmstad, Tillämpad matematik och fysik (CAMP), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-16027.
Full textAbstract:
Jump diffusion models are being used more and more often in financial applications. Consisting of a Brownian motion (with drift) and a jump component, such models have a number of parameters that have to be set at some level. Maximum Likelihood Estimation (MLE) turns out to be suitable for this task, however it is computationally demanding. For a complicated likelihood function it is seldom possible to find derivatives. The global maximum of a likelihood function defined for a jump diffusion model can however, be obtained by numerical methods. I chose to use the Bound Optimization BY Quadratic Approximation (BOBYQA) method which happened to be effective in this case. However, results of Maximum Likelihood Estimation (MLE) proved to be hard to interpret.
11
Yilmaz, Busra Zeynep. "Completion, Pricing And Calibration In A Levy Market Model." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612598/index.pdf.
Full textAbstract:
In this thesis, modelling with Lévy processes is considered in three parts. In the first part, the general geometric Lé
vy market model is examined in detail. As such markets are generally incomplete, it is shown that the market can be completed by enlarging with a series of new artificial assets called &ldquo
power-jump assets&rdquo
based on the power-jump processes of the underlying Lé
vy process. The second part of the thesis presents two different methods for pricing European options: the martingale pricing approach and the Fourier-based characteristic formula method which is performed via fast Fourier transform (FFT). Performance comparison of the pricing methods led to the fact that the fast Fourier transform produces very small pricing errors so the results of both methods are nearly identical. Throughout the pricing section jump sizes are assumed to have a particular distribution. The third part contributes to the empirical applications of Lé
vy processes. In this part, the stochastic volatility extension of the jump diffusion model is considered and calibration on Standard&
Poors (S&
P) 500 options data is executed for the jump-diffusion model, stochastic volatility jump-diffusion model of Bates and the Black-Scholes model. The model parameters are estimated by using an optimization algorithm. Next, the effect of additional stochastic volatility extension on explaining the implied volatility smile phenomenon is investigated and it is found that both jumps and stochastic volatility are required. Moreover, the data fitting performances of three models are compared and it is shown that stochastic volatility jump-diffusion model gives relatively better results.
12
Björnberg, Dag. "Modelling of Electricity Spot Prices : A Mean-Reverting Jump Diffusion Model Applied to the Nordic-Baltic Market." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-95326.
Full textAbstract:
This paper concerns the modelling of electricity spot prices in the Nordic-Baltic market. The paper begins with a description of the market and a summary of stylized facts of electricity spot prices. These characteristics are later on used in the calibration of a mean-reverting jump diffusion model. The work ends with simulations of the model and a discussion about further improvements that can be made.
13
Wang, Dong-Mei. "Monte Carlo simulations for complex option pricing." Thesis, University of Manchester, 2010. https://www.research.manchester.ac.uk/portal/en/theses/monte-carlo-simulations-for-complex-option-pricing(a908ec86-2fb2-4d5d-83e5-9bff78033edd).html.
Full textAbstract:
The thesis focuses on pricing complex options using Monte Carlo simulations. Due to the versatility of the Monte Carlo method, we are able to evaluate option prices with various underlying asset models: jump diffusion models, illiquidity models, stochastic volatility and so on. Both European options and Bermudan options are studied in this thesis.For the jump diffusion model in Merton (1973), we demonstrate European and Bermudan option pricing by the Monte Carlo scheme and extend this to multiple underlying assets; furthermore, we analyse the effect of stochastic volatility.For the illiquidity model in the spirit of Glover (2008), we model the illiquidity impact on option pricing in the simulation study. The four models considered are: the first order feedback model with constant illiquidity and stochastic illiquidity; the full feedback model with constant illiquidity and stochastic illiquidity. We provide detailed explanations for the present of path failures when simulating the underlying asset price movement and suggest some measures to overcome these difficulties.
14
Nadratowska, Natalia Beata, and Damian Prochna. "Option pricing under the double exponential jump-diffusion model by using the Laplace transform : Application to the Nordic market." Thesis, Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-5336.
Full textAbstract:
In this thesis the double exponential jump-diffusion model is considered and the Laplace transform is used as a method for pricing both plain vanilla and path-dependent options. The evolution of the underlying stock prices are assumed to follow a double exponential jump-diffusion model. To invert the Laplace transform, the Euler algorithm is used. The thesis includes the programme code for European options and the application to the real data. The results show how the Kou model performs on the NASDAQ OMX Stockholm Market in the case of the SEB stock.
15
Relvas, Ana Paula Gonçalves Couto. "Risco de crédito." Master's thesis, Instituto Superior de Economia e Gestão, 2018. http://hdl.handle.net/10400.5/17625.
Full textAbstract:
Mestrado em Mathematical FinanceEm resposta à crise da década de 70, os países do G10 criaram o Comité de Basileia, que fornece a regulamentação referente ao capital mínimo para os riscos incorridos. Este projeto resulta de um estágio no Banco Carregosa cujos objetivos são:validar o modelo económico de risco de crédito e verificar se reúne as condições para ser considerado um modelo multi-factor Vasicek; testar a adaptação ao modelo de Pedersen & Krogsgaard (2008); e analisar a rapidez e precisão do novo modelo. Estas propostas surgem da postura de melhoria contínua da instituição, em concreto, para uma gestão de riscos mais resiliente e realista. Procurou-se analisar, exaustivamente, o modelo utilizado e as possíveis adaptações pela integração do modelo estocástico de taxas de juro, da média reversível de índices de alavancagem dinâmicos, da antecipação de incumprimento e de saltos ao risco. Da análise feita ao modelo utilizado e às suas adaptações, assinala-se que os resultados gerados pelo modelo utilizado são sólidos e robustos. No entanto os resultados gerados pelas suas adaptações são demasiado fracos e muito sensíveis ao valor dos parâmetros adotados. Este estudo entende-se, também, pertinente, no contexto da crescente regulamentação e importância da análise do risco, num enquadramento de reduzido conhecimento disponível e de histórico comparável.
In response to the 70’s crisis, G10´s countries formed the Basel´s Committee that provides regulation about minimum capital to the risk incurred. This project is the outcome of an internship at Carregosa Bank (Banco Carregosa), and it has multiple purposes. Firstly, it is aimed to validate the economic model of credit risk and to verify if it satisfies the conditions to qualify as a multi-factor Vasicek model. It intends to test the adaptation of Pedersen & Krogsgaard (2008) model, and lastly to analyse the speed and accuracy of the new model. These proposals arise from an approach of continuous improvement of the institution, specifically for management of more resilient and realistic risks. There was an extensive analysis of the used model and the possible adaptations by the incorporation of the stochastic model of interest rates, mean reverting leverage ratios, early default and jump risks. Analysing the used model and its possible adaptations, it can be pointed out that the obtained results by the used model are strong and sound. Although, the obtained results by its adaptations are too weak and highly sensitive to the values of the adopted parameters. The study is also relevant in the context of increasing regulation and the importance of risk analysis in a framework of reduced knowledge available and comparable history.
info:eu-repo/semantics/publishedVersion
16
Paulin, Carl, and Maja Lindström. "Option pricing models: A comparison between models with constant and stochastic volatilities as well as discontinuity jumps." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-172226.
Full textAbstract:
The purpose of this thesis is to compare option pricing models. We have investigated the constant volatility models Black-Scholes-Merton (BSM) and Merton’s Jump Diffusion (MJD) as well as the stochastic volatility models Heston and Bates. The data used were option prices from Microsoft, Advanced Micro Devices Inc, Walt Disney Company, and the S&P 500 index. The data was then divided into training and testing sets, where the training data was used for parameter calibration for each model, and the testing data was used for testing the model prices against prices observed on the market. Calibration of the parameters for each model were carried out using the nonlinear least-squares method. By using the calibrated parameters the price was calculated using the method of Carr and Madan. Generally it was found that the stochastic volatility models, Heston and Bates, replicated the market option prices better than both the constant volatility models, MJD and BSM for most data sets. The mean average relative percentage error for Heston and Bates was found to be 2.26% and 2.17%, respectively. Merton and BSM had a mean average relative percentage error of 6.90% and 5.45%, respectively. We therefore suggest that a stochastic volatility model is to be preferred over a constant volatility model for pricing options.Syftet med denna tes är att jämföra prissättningsmodeller för optioner. Vi har undersökt de konstanta volatilitetsmodellerna Black-Scholes-Merton (BSM) och Merton’s Jump Diffusion (MJD) samt de stokastiska volatilitetsmodellerna Heston och Bates. Datat vi använt är optionspriser från Microsoft, Advanced Micro Devices Inc, Walt Disney Company och S&P 500 indexet. Datat delades upp i en träningsmängd och en test- mängd. Träningsdatat användes för parameterkalibrering med hänsyn till varje modell. Testdatat användes för att jämföra modellpriser med priser som observerats på mark- naden. Parameterkalibreringen för varje modell utfördes genom att använda den icke- linjära minsta-kvadratmetoden. Med hjälp av de kalibrerade parametrarna kunde priset räknas ut genom att använda Carr och Madan-metoden. Vi kunde se att de stokastiska volatilitetsmodellerna, Heston och Bates, replikerade marknadens optionspriser bättre än båda de konstanta volatilitetsmodellerna, MJD och BSM för de flesta dataseten. Medelvärdet av det relativa medelvärdesfelet i procent för Heston och Bates beräknades till 2.26% respektive 2.17%. För Merton och BSM beräknades medelvärdet av det relativa medelvärdesfelet i procent till 6.90% respektive 5.45%. Vi anser därför att en stokastisk volatilitetsmodell är att föredra framför en konstant volatilitetsmodell för att prissätta optioner.
17
Tassi-Londorfou, Eleftheria. "Jump diffusion models in volatility." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249634.
Full text
18
Londani, Mukhethwa. "Numerical Methods for Mathematical Models on Warrant Pricing." University of the Western Cape, 2010. http://hdl.handle.net/11394/8210.
Full textAbstract:
>Magister Scientiae - MScWarrant pricing has become very crucial in the present market scenario. See, for example, M. Hanke and K. Potzelberger, Consistent pricing of warrants and traded options, Review Financial Economics 11(1) (2002) 63-77 where the authors indicate that warrants issuance affects the stock price process of the issuing company. This change in the stock price process leads to subsequent changes in the prices of options written on the issuing company's stocks. Another notable work is W.G. Zhang, W.L. Xiao and C.X. He, Equity warrant pricing model under Fractional Brownian motion and an empirical study, Expert System with Applications 36(2) (2009) 3056-3065 where the authors construct equity warrants pricing model under Fractional Brownian motion and deduce the European options pricing formula with a simple method. We study this paper in details in this mini-thesis. We also study some of the mathematical models on warrant pricing using the Black-Scholes framework. The relationship between the price of the warrants and the price of the call accounts for the dilution effect is also studied mathematically. Finally we do some numerical simulations to derive the value of warrants.
19
Pszczola, Agnieszka, and Grzegorz Walachowski. "Testing for jumps in face of the financial crisis : Application of Barndorff-Nielsen - Shephard test and the Kou model." Thesis, Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-2872.
Full textAbstract:
The purpose of this study is to identify an impact on an option pricing within NASDAQ OMX Stockholm Market, if the underlying
asset prices include jumps. The current financial crisis, when jumps are much more evident than ever, makes this issue very actual and important in the global sense for the portfolio hedging and other risk management applications for example for the banking sector. Therefore, an investigation is based on OMXS30 Index and SEB A Bank. To detect jumps the Barndorff-Nielsen and Shephard non-parametric bipower variation test is used. First it is examined on simulations, to be finally implemented on the real data. An affirmation of a jumps occurrence requires to apply an appropriate model for the option pricing. For this purpose the Kou model, a double exponential jump-diffusion one, is proposed, as it incorporates essential stylized facts not available for another models. Th parameters in the model are estimated by a new approach - a combined cumulant matching with lambda taken from the Barrndorff-Nielsen and Shephard test. To evaluate how the Kou model manages on the option pricing, it is compared to the Black-Scholes model and to the real prices of European call options from the Stockholm Stock Exchange. The results show that the Kou model outperforms the latter.
20
Wickström, Simon. "Jump-Diffusion Models and Implied Volatility." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-242054.
Full text
21
Xu, Guoping. "Basket options pricing for jump diffusion models." Thesis, Imperial College London, 2010. http://hdl.handle.net/10044/1/6331.
Full textAbstract:
In this thesis we discuss basket option valuation for jump-diffusion models. We suggest three new approximate pricing methods. The first approximation method is the weighted sum of Rogers and Shi’s lower bound and the conditional second moment adjustments. The second is the asymptotic expansion to approximate the conditional expectation of the stochastic variance associated with the basket value process. The third is the lower bound approximation which is based on the combination of the asymptotic expansion method and Rogers and Shi’s lower bound. We also derive a forward partial integro-differential equation (PIDE) for general asset price processes with stochastic volatilities and stochastic jump compensators. Numerical tests show that the suggested methods are fast and accurate in comparison with Monte Carlo and other methods in most cases.
22
Fonseca, Francisco Maria de Mateus e. Jorge da. "Fractional diffusion models and option pricing in jump models." Master's thesis, Instituto Superior de Economia e Gestão, 2019. http://hdl.handle.net/10400.5/19086.
Full textAbstract:
Mestrado em Mathematical FinanceO problema de valorização de derivados tem sido o foco da investigação em Matemática Financeira desde a sua conceção. Mais recentemente, a literatura tem-se focado por exemplo em modelos que assumem que as dinâmicas do preço do ativo subjacente são governadas por um processo de Lévy (por vezes chamado um processo com saltos). Este tipo de modelo admite a possibilidade de eventos extremos (saltos), que não são devidamente capturados por modelos clássicos do tipo Black-Scholes, alicerçados no movimento Browniano. Foi também demonstrado ao longo da última década que se as dinâmicas do preço do ativo subjacente seguem certos processos de Lévy, tais como o CGMY , o FMLS e o KoBoL, os preços das opções satisfazem uma equação diferencial parcial fracionária. Nesta dissertação, iremos mostrar que se as dinâmicas do ativo subjacente seguem o denominado Processo Estável Temperado Generalizado, que admite como caso particular os suprareferidos processos CGMY e KoBoL, então os preços das opções satisfazem igualmente uma equação diferencial parcial fracionária. Além disso, iremos implementar um método simples de diferenças finitas para resolver numericamente a equação deduzida, e valorizar opções do tipo europeu.
The problem of pricing financial derivatives has been the focal point of research within the field of Mathematical Finance since its conception. In recent years, one of the main areas of focus within the literature has been on models which assume that the dynamics of the price of the underlying asset are governed by a Lévy process (sometimes referred to as a jump process). This type of model admits the possibility of extreme events (jumps), which are not captured by classical Black-Scholes type models based on the Brownian motion. Over the last decades, the literature has further shown that if the dynamics of the price of the underlying is governed by certain Lévy processes, such as the CGMY , the FMLS and the KoBoL, the price processes of European-style options satisfy a variety of fractional partial differential equations (FPDEs). In this dissertation, we will show that if the underlying price dynamic follows a Generalized Tempered Stable process, which admits as particular cases the aforementioned CGMY and KoBoL processes, prices of options satisfy an FPDE of the same type. Further, we will implement a simple finite difference scheme to solve the FPDE numerically to price European-type options.
info:eu-repo/semantics/publishedVersion
23
Zhou, Yu. "Option pricing and hedging in jump diffusion models." Thesis, Uppsala University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-125733.
Full text
24
Strauss, Arne Karsten. "Numerical Analysis of Jump-Diffusion Models for Option Pricing." Thesis, Virginia Tech, 2006. http://hdl.handle.net/10919/33917.
Full textAbstract:
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, discretize it implicitly using finite differences and the second order backward difference formula (BDF2) on a uniform grid. The arising dense linear system is solved by an iterative method, either a splitting technique or a circulant preconditioned conjugate gradient method. Exploiting the Fast Fourier Transform (FFT) yields the solution in only $O(n\log n)$ operations and just some vectors need to be stored. Second order accuracy is obtained on the whole computational domain for Merton's model whereas for Kou's model first order is obtained on the whole computational domain and second order locally around the strike price. The solution for the PIDE with convection term can oscillate in a neighborhood of the strike price depending on the choice of parameters, whereas the solution obtained from the transformed problem is stabilized.Master of Science
25
Yang, Yu. "Various Financial Applications of Regime-Switching Jump-Diffusion Models." Thesis, Curtin University, 2020. http://hdl.handle.net/20.500.11937/80427.
Full textAbstract:
The regime-switching jump-diffusion models have attracted great attention from the research community recently due to their ability to capture the random market movements during both short-term and long-term periods. This research focuses on the applications of various regime-switching jump-diffusion models to two important financial problems, the mean-variance asset-liability management problem and the pricing of variance (volatility) swaps, where little work has been done to our knowledge.
26
Johansson, Sam. "Efficient Monte Carlo Simulation for Counterparty Credit Risk Modeling." Thesis, KTH, Matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-252566.
Full textAbstract:
In this paper, Monte Carlo simulation for CCR (Counterparty Credit Risk) modeling is investigated. A jump-diffusion model, Bates' model, is used to describe the price process of an asset, and the counterparty default probability is described by a stochastic intensity model with constant intensity. In combination with Monte Carlo simulation, the variance reduction technique importance sampling is used in an attempt to make the simulations more efficient. Importance sampling is used for simulation of both the asset price and, for CVA (Credit Valuation Adjustment) estimation, the default time. CVA is simulated for both European and Bermudan options. It is shown that a significant variance reduction can be achieved by utilizing importance sampling for asset price simulations. It is also shown that a significant variance reduction for CVA simulation can be achieved for counterparties with small default probabilities by employing importance sampling for the default times. This holds for both European and Bermudan options. Furthermore, the regression based method least squares Monte Carlo is used to estimate the price of a Bermudan option, resulting in CVA estimates that lie within an interval of feasible values. Finally, some topics of further research are suggested.I denna rapport undersöks Monte Carlo-simuleringar för motpartskreditrisk. En jump-diffusion-modell, Bates modell, används för att beskriva prisprocessen hos en tillgång, och sannolikheten att motparten drabbas av insolvens beskrivs av en stokastisk intensitetsmodell med konstant intensitet. Tillsammans med Monte Carlo-simuleringar används variansreduktionstekinken importance sampling i ett försök att effektivisera simuleringarna. Importance sampling används för simulering av både tillgångens pris och, för estimering av CVA (Credit Valuation Adjustment), tidpunkten för insolvens. CVA simuleras för både europeiska optioner och Bermuda-optioner. Det visas att en signifikant variansreduktion kan uppnås genom att använda importance sampling för simuleringen av tillgångens pris. Det visas även att en signifikant variansreduktion för CVA-simulering kan uppnås för motparter med små sannolikheter att drabbas av insolvens genom att använda importance sampling för simulering av tidpunkter för insolvens. Detta gäller både europeiska optioner och Bermuda-optioner. Vidare, används regressionsmetoden least squares Monte Carlo för att estimera priset av en Bermuda-option, vilket resulterar i CVA-estimat som ligger inom ett intervall av rimliga värden. Slutligen föreslås några ämnen för ytterligare forskning.
27
Hauswirth, Christian. "Bond markets where the short rate is a jump diffusion /." [S.l.] : [s.n.], 1999. http://aleph.unisg.ch/hsgscan/hm00027422.pdf.
Full text
28
Merino, Fernández Raúl. "Option Price Decomposition for Local and Stochastic Volatility Jump Diffusion Models." Doctoral thesis, Universitat de Barcelona, 2021. http://hdl.handle.net/10803/671682.
Full textAbstract:
In this thesis, an option price decomposition for local and stochastic volatility jump diffusion models is studied. On the one hand, we generalise and extend the Alòs decomposition to be used in a wide variety of models such as a general stochastic volatility model, a stochastic volatility jump dffusion model with finite activity or a rough volatility model.
Furthermore, we note that in the case of local volatility models, speci_cally, spot-dependent models, a new decomposition formula must be used to obtain good numerical results. In particular, we study the CEV model. On the other hand, we observe that the approximation formula can be improved by using the decomposition formula recursively. Using this decomposition method, the call price can be transformed into a Taylor type formula containing an infinite series with stochastic terms. New approximation formulae are obtained in the Heston model case, finding better approximations.En aquesta tesi, s'estudia una descomposició del preu d'una opció per a models de volatilitat local i volatilitat estocàstica amb salts. D'una banda, generalitzem i estenem la descomposició d'Alòs per a ser utilitzada en una àmplia varietat de models com, per exemple, un model de volatilitat estocàstica general, un model de volatilitat estocàstica amb salts d'activitat finita o un model de volatilitat 'rough'. A més a més, veiern que en el cas dels models de volatilitat local, en particular, els models dependents del 'spot' s'ha d'utilitzar una nova fórmula de descomposició per a obtenir bons resultats numèrics. En particular, estudiem el model CEV. D'altra banda, observem que la fórmula d'aproximació es pot millorar utilitzant la formula de descomposició de forma recursiva. Mitjançant aquesta tècnica de descomposició, el preu d'una opció de compra es pot transformar en una formula tipus Taylor que conté una sèrie infinita de termes estocàstics. S'obtenen noves fórmules d'aproximació en el cas del model de Heston, trobant una millor aproximació.
En esta tesis, se estudia una descomposición del precio de una opción para los modelos de volatilidad local y volatilidad estocástica con saltos. Por un lado, generalizamos y ampliamos la descomposición de Alòs para ser utilizada en una amplia variedad de modelos como, por ejemplo, un modelo de volatilidad estocástica general, un modelo de volatilidad estocástica con saltos de actividad finita o un modelo de volatilidad 'rough'. Además, vemos que en el caso de los modelos de volatilidad local, en particular, los modelos dependientes del 'spot', se debe utilizar una nueva fórmula de descomposición para obtener buenos resultados numéricos. En particular, estudiamos el modelo CEV. Por otro lado, observamos que la fórmula de aproximación se puede mejorar utilizando la fórmula de descomposición de forma recursiva. Mediante esta técnica de descomposición, el precio de una opción de compra se puede transformar en una fórmula tipo Taylor que contiene una serie infinita de términos estocásticos. Se obtienen nuevas fórmulas de aproximación en el caso del modelo de Heston, encontrando una mejor aproximación.
29
Lahiri, Joydeep. "Affine jump diffusion models for the pricing of credit default swaps." Thesis, University of Reading, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.529979.
Full text
30
Zhang, Xiang. "Essays on empirical performance of affine jump-diffusion option pricing models." Thesis, University of Oxford, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.552834.
Full textAbstract:
This thesis examines the empirical performance of option pricing models in the continuous- time affine jump-diffusion (AID) class. In models of this class, the underlying returns are governed by stochastic volatility diffusions and/or jumps and the dynamics of the whole system has affine dependence on the state variables. The thesis consists of three essays. The first essay calibrates a wide range of AID option pricing models to S&P 500 index options. The aim is to empirically identify how best to structure two types of risk components- stochastic volatility and jumps - within the framework of multi-factor AID specifications. Our specification analysis shows that the specifications with more-than-two diffusions perform well and that a three-factor specification should be preferred, in which jump intensities are allowed to depend on an independent diffusion process. Having identified the well-performing pricing model specifications, the second essay examines how such a model can be used to forecast realized volatility using only option prices as an input. To do so, the dynamics of volatility implied by the model are used to construct a forecasting equation in which the spot volatilities extracted from observed option prices act as the key predictors. The analysis indicates that the option-based multi-factor forecasting model outperforms other popular models in forecasting realized volatility of S&P 500 Index returns over most of the short-term horizons considered. The final essay investigates if a two-factor AJD model can fit option pricing patterns generated by a single-factor long memory volatility model. Our simulation experiments show that this model does well in this respect. Remarkably, however, at the fitted parameter values it does not generate the volatility auto-correlation patterns that are characteristic of long-memory volatility models.
31
Xu, Li. "Financial and computational models in electricity markets." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51849.
Full textAbstract:
This dissertation is dedicated to study the design and utilization of financial contracts and pricing mechanisms for managing the demand/price risks in electricity markets and the price risks in carbon emission markets from different perspectives. We address the issues pertaining to the efficient computational algorithms for pricing complex financial options which include many structured energy financial contracts and the design of economic mechanisms for managing the risks associated with increasing penetration of renewable energy resources and with trading emission allowance permits in the restructured electric power industry. To address the computational challenges arising from pricing exotic energy derivatives designed for various hedging purposes in electricity markets, we develop a generic computational framework based on a fast transform method, which attains asymptotically optimal computational complexity and exponential convergence. For the purpose of absorbing the variability and uncertainties of renewable energy resources in a smart grid, we propose an incentive-based contract design for thermostatically controlled loads (TCLs) to encourage end users' participation as a source of DR. Finally, we propose a market-based approach to mitigate the emission permit price risks faced by generation companies in a cap-and-trade system. Through a stylized economic model, we illustrate that the trading of properly designed financial options on emission permits reduces permit price volatility and the total emission reduction cost.
32
Zhang, Lei. "An empirical analysis of jump diffusion stochastic volatility models for currency option pricing." Thesis, University of Nottingham, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.546561.
Full text
33
Timsina, Tirtha Prasad. "Sensitivities in Option Pricing Models." Diss., Virginia Tech, 2007. http://hdl.handle.net/10919/28904.
Full textAbstract:
The inverse problem in finance consists of determining the unknown parameters of
the pricing equation from the values quoted from the market. We formulate the
inverse problem as a minimization problem for an appropriate cost function to minimize
the difference between the solution of the model and the market observations.
Efficient gradient based optimization requires accurate gradient estimation of the
cost function. In this thesis we highlight the adjoint method for computing gradients
of the cost function in the context of gradient based optimization and show its
importance. We derive the continuous adjoint equations with appropriate boundary
conditions for three main option pricing models: the Black-Scholes model, the Hestonâ 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 function F(¾)
with respect to parameters ¾ where F depends on ¾ indirectly, via an intermediate
variable. Compared to the finite difference method and the sensitivity equation
method, the adjoint equation method is very efficient in computing the gradient
of the cost function. The sensitivity equations method requires solving a PDE
corresponding to each parameter in the model to estimate the gradient of the cost
function. The adjoint method requires solving a single adjoint equation once. Hence,
for a large number of parameters in the model, the adjoint equation method is very
efficient.
Due to its nature, the adjoint equation has to be solved backward in time. The
adjoint equation derived from the jump diffusion model is harder to solve due to its
non local integral term. But algorithms that can be used to solve the Partial Integro-
Differential Equation (PIDE) derived from jump diffusion model can be modified to
solve the adjoint equation derived from the PIDE.Ph. D.
34
Gleeson, Cameron Banking & Finance Australian School of Business UNSW. "Pricing and hedging S&P 500 index options : a comparison of affine jump diffusion models." Awarded by:University of New South Wales. School of Banking and Finance, 2005. http://handle.unsw.edu.au/1959.4/22379.
Full textAbstract:
This thesis examines the empirical performance of four Affine Jump Diffusion models in pricing and hedging S&P 500 Index options: the Black Scholes (BS) model, Heston???s Stochastic Volatility (SV) model, a Stochastic Volatility Price Jump (SVJ) model and a Stochastic Volatility Price-Volatility Jump (SVJJ) model. The SVJJ model structure allows for simultaneous jumps in price and volatility processes, with correlated jump size distributions. To the best of our knowledge this is the first empirical study to test the hedging performance of the SVJJ model. As part of our research we derive the SVJJ model minimum variance hedge ratio. We find the SVJ model displays the best price prediction. The SV model lacks the structural complexity to eliminate Black Scholes pricing biases, whereas our results indicate the SVJJ model suffers from overfitting. Despite significant evidence from in and out-of-sample pricing that the SV and SVJ models were better specified than the BS model, this did not result in an improvement in dynamic hedging performance. Overall the BS delta hedge and SV minimum variance hedge produced the lowest errors, although their performance across moneyness-maturity categories differed greatly. The SVJ model???s results were surprisingly poor given its superior performance in out-of-sample pricing. We attribute the inadequate performance of the jump models to the lower hedging ratios these models provided, which may be a result of the negative expected jump sizes.
35
Hrbek, Filip. "Metody předvídání volatility." Master's thesis, Vysoká škola ekonomická v Praze, 2015. http://www.nusl.cz/ntk/nusl-264689.
Full textAbstract:
In this masterthesis I have rewied basic approaches to volatility estimating. These approaches are based on classical and Bayesian statistics. I have applied the volatility models for the purpose of volatility forecasting of a different foreign exchange (EURUSD, GBPUSD and CZKEUR) in the different period (from a second period to a day period). I formulate the models EWMA, GARCH, EGARCH, IGARCH, GJRGARCH, jump diffuison with constant volatility and jump diffusion model with stochastic volatility. I also proposed an MCMC algorithm in order to estimate the Bayesian models. All the models we estimated as univariate models. I compared the models according to Mincer Zarnowitz regression. The most successfull model is the jump diffusion model with a stochastic volatility. On the second place they were the GJR- GARCH model and the jump diffusion model with a constant volatility. But the jump diffusion model with a constat volatilit provided much more overvalued results.The rest of the models were even worse. From the rest the IGARCH model is the best but provided undervalued results. All these findings correspond with R squared coefficient.
36
Yang, Cheng-Yu. "Essays on multi-asset jump diffusion models : estimation, asset allocation and American option pricing." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/93986/.
Full textAbstract:
In the first essay (Chapter 2), we develop an efficient payoff function approximation approach to estimating lower and upper bounds for pricing American arithmetic average options with a large number of underlying assets. This method is particularly efficient for asset prices modeled by jump-diffusion processes with deterministic volatilities because the geometric mean is always a one-dimensional Markov process regardless of the number of underlying assets and thus is free from the curse of dimensionality. Another appealing feature of our method is that it provides an extremely efficient way to obtain tight upper bounds with no nested simulation involved as opposed to some existing duality approaches. Various numerical examples with up to 50 underlying stocks suggest that our algorithm is able to produce computationally efficient results. Chapter 3 solves portfolio choice problem in multi-dimensional jump-diffusion models designed to capture empirical features of stock prices and financial contagion effect. To obtain closed-form solution, we develop a novel general decomposition technique with which we reduce the problem into two relative simple ones: Portfolio choice in a pure-diffusion market and in a jump-diffusion market with less dimension. The latter can be reduced further to be a bunch of portfolio choice problems in one-dimensional jump-diffusion markets. By virtue of the decomposition, we obtain a semi-closed form solution for the primary optimal portfolio choice problem. Our solution provides new insights into the structure of an optimal portfolio when jumps are present in asset prices and/or their variance-covariance. In Chapter 4, we develop a estimation procedure based on Markov Chain Monte Carlo methods and aim to provide systematic ways to estimating general multivariate stochastic volatility models. In particular, this estimation technique is proved to be efficient for multivariate jump-diffusion process such as the model developed in Chapter 3 with various simulation studies. As a result, it contributes to the asset pricing literature by providing an efficient estimation technique for asset pricing models.
37
Bosserhoff, Frank [Verfasser]. "Portfolio selection, delta hedging and robustness in Brownian and jump-diffusion models / Frank Bosserhoff." Ulm : Universität Ulm, 2020. http://d-nb.info/1206248602/34.
Full text
38
Liu, Xin. "Fast exponential time integration scheme and extrapolation method for pricing option with jump diffusions." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148264.
Full text
39
Ezzine, Ahmed. "Some topics in mathematical finance. Non-affine stochastic volatility jump diffusion models. Stochastic interest rate VaR models." Doctoral thesis, Universite Libre de Bruxelles, 2004. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211156.
Full text
40
Lu, Bing. "Calibration, Optimality and Financial Mathematics." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-209235.
Full textAbstract:
This thesis consists of a summary and five papers, dealing with financial applications of optimal stopping, optimal control and volatility. In Paper I, we present a method to recover a time-independent piecewise constant volatility from a finite set of perpetual American put option prices. In Paper II, we study the optimal liquidation problem under the assumption that the asset price follows a geometric Brownian motion with unknown drift, which takes one of two given values. The optimal strategy is to liquidate the first time the asset price falls below a monotonically increasing, continuous time-dependent boundary. In Paper III, we investigate the optimal liquidation problem under the assumption that the asset price follows a jump-diffusion with unknown intensity, which takes one of two given values. The best liquidation strategy is to sell the asset the first time the jump process falls below or goes above a monotone time-dependent boundary. Paper IV treats the optimal dividend problem in a model allowing for positive jumps of the underlying firm value. The optimal dividend strategy is of barrier type, i.e. to pay out all surplus above a certain level as dividends, and then pay nothing as long as the firm value is below this level. Finally, in Paper V it is shown that a necessary and sufficient condition for the explosion of implied volatility near expiry in exponential Lévy models is the existence of jumps towards the strike price in the underlying process.
41
Krebs, Daniel. "Pricing a basket option when volatility is capped using affinejump-diffusion models." Thesis, KTH, Matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-123395.
Full textAbstract:
This thesis considers the price and characteristics of an exotic option called the Volatility-Cap-Target-Level(VCTL) option. The payoff function is a simple European option style but the underlying value is a dynamic portfolio which is comprised of two components: A risky asset and a non-risky asset. The non-risky asset is a bond and the risky asset can be a fund or an index related to any asset category such as equities, commodities, real estate, etc. The main purpose of using a dynamic portfolio is to keep the realized volatility of the portfolio under control and preferably below a certain maximum level, denoted as the Volatility-Cap-Target-Level (VCTL). This is attained by a variable allocation between the risky asset and the non-risky asset during the maturity of the VCTL-option. The allocation is reviewed and if necessary adjusted every 15th day. Adjustment depends entirely upon the realized historical volatility of the risky asset. Moreover, it is assumed that the risky asset is governed by a certain group of stochastic differential equations called affine jump-diffusion models. All models will be calibrated using out-of-the money European call options based on the Deutsche-Aktien-Index(DAX). The numerical implementation of the portfolio diffusions and the use of Monte Carlo methods will result in different VCTL-option prices. Thus, to price a nonstandard product and to comply with good risk management, it is advocated that the financial institution use several research models such as the SVSJ- and the Seppmodel in addition to the Black-Scholes model. Keywords: Exotic option, basket option, risk management, greeks, affine jumpdiffusions, the Black-Scholes model, the Heston model, Bates model with lognormal jumps, the Bates model with log-asymmetric double exponential jumps, the Stochastic-Volatility-Simultaneous-Jumps(SVSJ)-model, the Sepp-model.
42
Chang, Yu-Chun, and 張育群. "Pricing American options in the jump diffusion model." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/73701399441213150102.
Full text
43
Ming-HsuanTsai and 蔡明軒. "Jump Diffusion Model with Asymmetry ofVolatility for VaR." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/95179194741944633790.
Full textAbstract:
碩士國立成功大學
統計學系碩博士班
101
Financial asset returns have some characteristics of leptokurticity and skewness. Traditional normality assumption of the return distribution couldn’t describe this phenomenon. What’s more, financial asset returns are often affected by external factors which lead to instant price jumps. Jump diffusion models therefore attract more and more attention. This thesis modifies the asymmetric double-exponential jump-amplitude model proposed by Kou(Kou, 2002) and combines it with the GJR-GARCH volatility model. The result of this research is compared with the Kou (Kou, 2002) and Hanson ＆ Westman (Hanson ＆ Westman, 2002) jump models. Our empirical study on TAIEX index data shows the proposed model gives more accurate VaR.
44
Wang, Shih-Hung, and 王士宏. "Pricing EDS Based on Merton Jump-diffusion Model." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/25040832566976195509.
Full textAbstract:
碩士國立高雄第一科技大學
金融所
98
In recent years, the emergence of credit derivative products has been developed as the result of the rapid development of derivative products. Among them, credit default swaps has the largest trading volume over the global market. The latest new product has been developed substituting for credit default swaps in the market, known as equity default swaps. Due to the fact that stock price does not always act as a continuous process, sometimes an unusual jump exists in some situations like major news will give rise to the stock price change sharply. Therefore, in order to capture the sudden changes in firm’s asset value, we use jump-diffusion model by Merton (1976) for pricing and we also compared the performance with Merton (1974) diffusion model. Moreover, by using the EM algorithm, the problem of unobservable firm’s asset value under Merton (1974) and Merton (1976) is overcome by Duan, Gauthier and Simonato (2004), and Wong and Li (2006) respectively. EM algorithm is then applied to estimate the parameters required for pricing and calculating a reasonable EDS spread. Furthermore, we also do the sensitivity analysis of factors which would affect the EDS spread.
45
Liao, Yun-Jhen, and 廖允禎. "Pricing Contingent Capital under a Jump Diffusion Model." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/2wj8sa.
Full textAbstract:
碩士國立交通大學
財務金融研究所
106
Contingent capital is the type of special debt that converts to equity under some conditions. We consider that contingent convertible bonds with a capital-ratio trigger under double exponential jumps diffusion model. We derive closed-form of Laplace transform for market values. Therefore, we compute the market values by a Laplace inversion algorism. We can make sensitivity analysis under this type jump diffusion model comparing to the case without jumps.
46
Sheng-Feng, Luo. "Pricing Discrete Barrier Options Under A Jump-Diffusion Model." 2006. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-0507200611285600.
Full text
47
Wang, Ching-Ya, and 王靖雅. "Pricing Catastrophe Equity Put under Jump Diffusion Tree Model." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/bu2z8y.
Full text
48
Luo, Sheng-Feng, and 羅盛豐. "Pricing Discrete Barrier Options Under A Jump-Diffusion Model." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/09019957088054409141.
Full textAbstract:
碩士國立臺灣大學
財務金融學研究所
94
The payoff of a barrier option depends on whether a specified underlying asset price crosses a specified level (called a barrier) during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier. However, in practice, many real contracts with barrier provisions specify discrete monitoring times. Such options are called discrete barrier options. Broadie et al. (1997) showed that discrete barrier options can be priced using continuous barrier formulas by applying a simple continuity correction to the barrier under the geometric Brownian motion setting. In this article, we focus on the connection between the discrete and continuous barrier options using the same method of correction to the barrier but under the constant jump diffusion model. The correction is justified theoretically by applying the techniques from sequential analysis, particularly Siegmund (1985). And we also give numerical results.
49
Sun, Pai-Ching, and 孫百慶. "Applying Merton Jump Diffusion Model in Financial Distress Prediction." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/88997394532241821719.
Full textAbstract:
碩士國立高雄第一科技大學
金融所
98
The empirical evidence shows that the existence of fat-tail or jump in many financial assets return or assets value distribution is a really common phenomenon. In this paper, we try to add a jump component in order to describe the sudden drop or increase in firm’s asset value, so we consider the well-know jump diffusion process in setting the asset dynamic process for capturing the discontinuousness of asset value. As for the parameters estimation, we rely on the method called EM algorithm instead of maximum likelihood estimation. Finally, we calculate the risk neutral default probability under Merton jump model and constructed a default risk predictive model. In this study, we also compare the prediction performance to the commonly adopted model, Merton model, Z-score model and even the new version of Z-score model. We find evidence that the Z-score models outperform our default predictive model. And between the prediction performance of our model and of the traditional Merton model, we cannot tell which one is better off.
50
Chang, Syu-Teng, and 張緒漛. "EDS PRICING WITH STOCHASTIC VOLATILITY AND JUMP DIFFUSION MODEL." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/41488386819392310435.
Full textAbstract:
碩士國立高雄第一科技大學
金融系碩士班
105
The purpose of this paper is to examines the improvement of pricing Equity Default Swaps via Stochastic Volatility and Jump Diffusion model (SVJ , Bates (1996)).We use the Marginalized Resample-move(MRM)algorithm to estimate the unknown parameters of the SV and the SVJ model. And, the results of empirical analysis shows that the impact of EDS spreads from jumps. Thus, the model which is more pragmatic had been chosen to do the parameters sensitivity analysis for EDS spreads. This is helpful for measuring and predicting the corporate structural credit risk.