Pricing Model of Credit Default Swap Based on Jump-Diffusion Process and Volatility with Markov Regime Shift

By introducing the Jump-Diffusion Process and Markov Regime Shift, the paper explores Monte Carlo simulation to examine the pricing problem of single name Credit Default Swaps (CDS), which the price of CDS is affected by both unpredictable idiosyncratic risk and system risk caused by the macroeconomic change. The study shows that the price of CDS increases as the intensity and the amplitude of the Jump-Diffusion Process increase. Furthermore, the CDS price depends on the initial state and transition intensity of the volatility of the corporate value, which the former can reflect the influence of macroeconomic situation

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

CDS Pricing with Counterparty Risk

This thesis focuses on the impact of counterparty-risk in CDS (Credit Default Swap) pricing. The exponential growth of the Credit Derivatives Market in the last decade demands an upsurge in the fair valuation of various credit derivatives such as the Credit Default Swap (CDS), the Collateralized Debt Obligation (CDO). Financial institutions suffered great losses from Credit Derivatives in the sub-prime mortgage market during the credit crunch period. Counterparty risk in CDS contracts has been intensively studied with a focus on losses for protection buyers due to joint defaults of counterparty and reference entity. Using a contagion framework introduced by Jarrow and Yu (2001)[48], we calculate the swap premium rate based on the change of measure technique, and further extend both the two-firm and three-firm model (with defaultable protection buyer) with continuous premium payment. The results show more explanatory power than the discrete case. We improve the continuous contagion model by relaxing the constant intensity rate assumption and found close results without loss of generality. Empirically this thesis studies the behaviour of the historical credit spread of 55 sample corporates/ financial institutions, a Cox–Ingersoll–Ross model is applied to calibrate spread parameters. A proxy for counterparty spread is introduced as the difference between the spread over benchmark rate and spread over swap rate for 5 year maturity CDS. We then investigate counterparty risk during the crisis and study the shape of term structure for the counterparty spread, where Rebonato’s framework is deployed to model the dynamics of the term structure using a regime-switching framework

Essays in Financial and Insurance Mathematics.

This dissertation consists of the following three parts: (i) We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset. The price of the risky asset is assumed to follow a diffusion with stochastic volatility. Given the rate of consumption, we find the optimal investment strategy for the individual who wishes to minimize the probability of outliving the wealth. Techniques from stochastic optimal control are used. (ii) We extend the Heston stochastic volatility model to include state-dependent jumps in the price and the volatility, and develop a method for the exact simulation of this model. The jumps arrive with a stochastic intensity that may depend on time, price, volatility and jump counts. The jumps may have an impact on the price or the volatility, or both. The random jump size may depend on the price and volatility. The exact simulation method is based on projection and point process filtering arguments. Numerical experiments illustrate the features of the exact method. (iii) We study the properties of sovereign credit risk using Credit Default Swap (CDS) spreads for U.S. and major sovereign countries. We develop a regime-switching two-factor model that allows for both global-systemic and sovereign-specific credit shocks, and use maximum likelihood estimation to calibrate model parameters to weekly CDS data. The preliminary results suggest that there is heterogeneity across different countries with respect to their sensitivity to system risk. Furthermore, the high-volatility and low-volatility regimes behave differently with asymmetric regime-shift probabilities.Ph.D.Applied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91381/1/xyhu_1.pd

Applications of hidden Markov models in financial modelling

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.Various models driven by a hidden Markov chain in discrete or continuous time are developed to capture the stylised features of market variables whose levels or values constitute as the underliers of financial derivative contracts or investment portfolios. Since the parameters are switching regimes, the changes and developments in the economy as soon as they arise are readily reflected in these models. The change of probability measure technique and the EM algorithm are fundamental techniques utilised in the optimal parameter estimation. Recursive adaptive filters for the state of the Markov chain and other auxiliary processes related to the Markov chain are derived which in turn yield self-tuning dynamic financial models. A hidden Markov model (HMM)-based modelling set-up for commodity prices is developed and the predictability of the gold market under this setting is examined. An Ornstein-Uhlenbeck (OU) model with HMM parameters is proposed and under this set-up, we address two statistical inference issues: the sensitivity of the model to small changes in parameter estimates and the selection of the optimal number of states. The extended OU model is implemented on a data set of 30-day Canadian T-bill yields. An exponential of a Markov-switching OU process plus a compound Poisson process is put forward as a model for the evolution of electricity spot prices. Using a data set compiled by Nord Pool, we illustrate the vast improvements gained in incorporating regimes in the model. A multivariate HMM is employed as a framework in providing the solutions of two asset allocation problems; one involves the mean-variance utility function and the other entails the CVaR constraint. Finally, the valuation of credit default swaps highlights the important considerations necessitated by pricing in a regime-switching environment. Certain numerical schemes are applied to obtain approximations for the default probabilities and swap rates.Brunel Research Initiative and Enterprise Fund (BRIEF) and European Union (Marie Curie Fellowship

金融証券市場に関する研究 : 価格、意思決定および実証分析

首都大学東京, 2015-09-30, 博士（経営学）, 甲第553号首都大学東

Term Structure of Default-Free and Defaultable Securities: Theory and Empirical Evidence

This article provides a survey on term structure models designed for pricing fixed income securities and their derivatives. 1 The past several decades have witnessed a rapid development in the fixed-income markets. A number of new fixed-income instruments have been introduced successfully into the financial market. These include, to mention just a few, strips, debt warrants, put bonds, commercial mortgage-backed securities, payment-in-kind debentures, zero-coupon convertibles, interest rate futures and options, credit default swaps, and swaptions. The size of the fixed-income market has greatly expanded. The total value of the fixed-income assets is about two-thirds of the market value of all outstanding securities.2 From the investment perspective, it is important to understand how fixed-income securities are priced. The term structure of interest rates plays a key role in pricing fixed income securities. Not surprisingly, a vast literature has been devoted to understanding the stochastic behavior of term structure of interest rate, the pricing mechanism of fixed-income markets, and the spread between different fixed-income securities. Past research generally focuses on: (i) modeling the term structure of interest rates and yield spreads; (ii) providing empirical evidence; and (iii) applying the theory to the pricing of fixed-income instruments and risk management. As such, our review centers on alternative models of term structure of interest rates, their tractability, empirical performance, and applications. We begin with the basic definitions and notations in Section 1. We provide clear concepts of term structure of interest rates that are easily misunderstood. Section 2 introduces bond pricing theory within the dynamic term structure model (DTSM) framework. This framework provides a general modeling structure in which most of the popular term structure models are nested. This discussion thus helps understand the primary ingredients to categorize different DTSMs, i.e., the risk-neutral distribution of the state variables and the mapping function between these state variables and instantaneous interest rate. Sections 3 provides a literature review of the studies on default free bonds. Several widely used continuous-time DTSMs are reviewed here, including affine, quadratic, regime switching, jump-diffusion and stochastic volatility models. We conclude this section with a discussion of empirical performance of these DTSMs, where we discuss some open issues, including the expectation puzzle, the linearity of state variables, the advantages of multifactor and nonlinear models, and their implications for pricing and risk management. The studies of defaultable bonds are explored in section 4. We review both structural and reduced-form models, with particular attention given to the later. Several important issues in reduced form models are addressed here, including the specification of recovery rates, default intensity, coupon payment, other factors such as liquidity and taxes, and correlated defaults. Since it is convenient to have a closed-form pricing formula, it is important to evaluate the tradeoff between analytical tractability and the model complexity. Major empirical issues are related touncovering the components of yield spreads and answering the question whether the factors are latent or observable. Section 5 reviews the studies on two popular interest rate derivatives: interest rate swap and credit default swap. Here we present the pricing formulas of interest rate swap and credit default swap based on risk-neutral pricing theory. Other risk factors, such as counterparty risk and liquidity risk are then introduced into the pricing formula. Following this, we review important empirical work on the determinants of interest rate swap spread and credit default swap spread. Section 6 concludes the paper by providing a summary of the literature and directions for future research. These include: (i) the economic significance of DTSM specification on pricing and risk management; (ii) the difference of interest rate dynamics in the risk neutral measure and physical measure; (iii) the decomposition of yield spreads; and (iv) the pricing of credit risk with correlated factors.This article is forthcoming in Handbook of Quantitative Finance and Risk Management, edited by C.F. Lee and A. Lee. Spring Publisher.

Modelling spread risk via time-change approach

The thesis considers two stochastic models for managing spread risk: i) the Duffie-Singleton model; ii) a model developed in the context of electricity spot price modelling, properly adapted to model spread risk, obtained by changing the Duffie-Singleton model with compound Poisson’s jumps with exponentially distributed jump size and a subordinated process as a random clock. The latter has a mean reverting jump component that leads to mean reversion in the level of credit spread in addition to the smooth mean reversion force. In order to calibrate the models the particle filtering technique is used, which allows for the estimate of real-world and risk-neutral probability distributions from time series of credit spread observations

Essays on the credit default swap market

The focus of this dissertation is the European Credit Default Swaps (CDSs) market. CDSs are the most popular credit derivative products. Three issues are discussed, the first, which is covered in chapter 2, is the investigation of non-diversifiable jump risk in iTraxx sector indices based on a multivariate model that explicitly admits discrete common jumps for an index and its components. Our empirical research shows that both the iTraxx Non-Financials and their components experience jumps during the sample period, which means that the jump risks in the iTraxx sector index are not diversifiable. The second issue, which is covered in chapter 3 is the component structure of credit default swap spreads and their determinants. We firstly extract a transitory component and a persistent component from two different maturities of the Markit iTraxx index and then regress these components against proxies for several commonly used explanatory variables. Our results show that these explanatory variables have significant but differing impacts on the extracted components, which indicates that a two-factor formulation may be needed to model CDS options. The last issue, which is covered in chapters 4, 5 and 6 is the investigation of the linkage between the credit default swap market and the equity market within the European area. We innovatively calibrate the CDS option with the Heston Model to get the implied volatility in the CDS market, which allows us to investigate both the characteristic of implied volatility in the CDS market and the relationship of the two markets not only on the level of daily changes but also with regard to its second moment. Our analysis shows that the stock market weakly leads the CDS market on daily changes but for implied volatility, the stock market leads the CDS market. A VECM analysis shows that only the stock market contributes to price discovery. For sub-investment grade entities, the interactivities between the implied volatility of the CDS market and the implied volatility of the stock market are stronger, especially during the recent credit crunch period. All these results have important implications for the construction of portfolios with credit-sensitive instruments

Applications of hidden Markov models in financial modelling

Various models driven by a hidden Markov chain in discrete or continuous time are developed to capture the stylised features of market variables whose levels or values constitute as the underliers of financial derivative contracts or investment portfolios. Since the parameters are switching regimes, the changes and developments in the economy as soon as they arise are readily reflected in these models. The change of probability measure technique and the EM algorithm are fundamental techniques utilised in the optimal parameter estimation. Recursive adaptive filters for the state of the Markov chain and other auxiliary processes related to the Markov chain are derived which in turn yield self-tuning dynamic financial models. A hidden Markov model (HMM)-based modelling set-up for commodity prices is developed and the predictability of the gold market under this setting is examined. An Ornstein-Uhlenbeck (OU) model with HMM parameters is proposed and under this set-up, we address two statistical inference issues: the sensitivity of the model to small changes in parameter estimates and the selection of the optimal number of states. The extended OU model is implemented on a data set of 30-day Canadian T-bill yields. An exponential of a Markov-switching OU process plus a compound Poisson process is put forward as a model for the evolution of electricity spot prices. Using a data set compiled by Nord Pool, we illustrate the vast improvements gained in incorporating regimes in the model. A multivariate HMM is employed as a framework in providing the solutions of two asset allocation problems; one involves the mean-variance utility function and the other entails the CVaR constraint. Finally, the valuation of credit default swaps highlights the important considerations necessitated by pricing in a regime-switching environment. Certain numerical schemes are applied to obtain approximations for the default probabilities and swap rates.EThOS - Electronic Theses Online ServiceBrunel Research Initiative and Enterprise Fund (BRIEF) : European Union (Marie Curie Fellowship)GBUnited Kingdo