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Identifying realized jumps on financial markets
, 2006
"... This paper extends the jump detection method based on bipower variation and swap variance measures to identify realized jumps on financial markets and to estimate parametrically the jump intensity, mean, and variance. Such an approach does not require specifying and estimating the underlying drift ..."
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This paper extends the jump detection method based on bipower variation and swap variance measures to identify realized jumps on financial markets and to estimate parametrically the jump intensity, mean, and variance. Such an approach does not require specifying and estimating the underlying drift and diffusion functions. Finite sample evidence suggests that the jump parameters can be accurately estimated and that the statistical inferences can be reliable relative to the maximum likelihood estimation, under the appropriate choice of jump detection test level and assuming that jumps are rare and large. The bipower variation approach performs slightly better than the swap variance approach when the jump contribution to total variance is small. Applications to equity market, treasury bond, individual stock, and exchange rate reveal important differences in jump frequencies and volatilities across asset classes over time. For high investment grade credit spread indices, the estimated jump volatility has a better forecasting power than interest rate factors, volatility factors including optionimplied volatility, and FamaFrench risk factors.
2009, Pricing Credit Derivatives under Incomplete Information: a NonlinearFiltering Approach
"... Abstract This paper considers a general reduced form pricing model for credit derivatives where default intensities are driven by some factor process X. The process X is not directly observable for investors in secondary markets; rather, their information set consists of the default history and of n ..."
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Abstract This paper considers a general reduced form pricing model for credit derivatives where default intensities are driven by some factor process X. The process X is not directly observable for investors in secondary markets; rather, their information set consists of the default history and of noisy price observation for traded credit products. In this context the pricing of credit derivatives leads to a challenging nonlinear filtering problem. We provide recursive updating rules for the filter, derive a finite dimensional filter for the case where X follows a finite state Markov chain and propose a novel particle filtering algorithm. A numerical case study illustrates the properties of the proposed algorithms.
Large Portfolio Losses: A Dynamic Contagion Model
 Annals of Applied Probability
"... Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute th ..."
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Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute the limiting distributions of the system and determine the time evolution of the credit quality indicators of the firms, deriving moreover the dynamics of a global financial health indicator. We finally describe a suitable version of the “Central Limit Theorem ” useful to study large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis. 1. Introduction. 1.1. General aspects. The main purpose of this paper is to describe propagation of financial distress in a network of firms linked by business relationships. Once the model for financial contagion has been described, we quantify the impact of contagion on the losses suffered by a financial institution
Credit Risk Models with Incomplete Information
, 2007
"... Incomplete information is at the heart of informationbased credit risk models. In this paper, we rigorously define incomplete information with the notion of “delayed filtrations”. We characterize two distinct types of delayed information, continuous and discrete: the first generated by a time chang ..."
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Cited by 15 (0 self)
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Incomplete information is at the heart of informationbased credit risk models. In this paper, we rigorously define incomplete information with the notion of “delayed filtrations”. We characterize two distinct types of delayed information, continuous and discrete: the first generated by a time change of filtrations and the second by finitely many marked point processes. This notion unifies the noisy information in Duffie and Lando (2001) and the partial information in CollinDufresne et al. (2004), under which structural models are translated into reducedform intensitybased models. We illustrate through a simple example the importance of this notion of delayed information, as well as the potential pitfall for abusing the Laplacian approximation techniques for calculating the intensity process in an informationbased model. The authors are grateful to the Associate Editor and the two anonymous referees for their constructive suggestions and enlightening remarks.
Correlated Default Risk
, 2006
"... Recently, an unusually high number of firms in the economy defaulted, with the default rate for Moody’srated speculativegrade issuers reaching as high as 10.2 % in 2001. In their annual review, Moody’s summarized these credit events as follows, “Record defaults —unmatched in number and dollar volum ..."
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Cited by 14 (2 self)
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Recently, an unusually high number of firms in the economy defaulted, with the default rate for Moody’srated speculativegrade issuers reaching as high as 10.2 % in 2001. In their annual review, Moody’s summarized these credit events as follows, “Record defaults —unmatched in number and dollar volume since the Great Depression—have culminated in the bankruptcies of wellknown firms whose rapid collapse caught investors by surprise. ” 1 What factors cause the economywide default rate to change over time, and why does it vary as much as it does? In this article, we investigate the likelihood of joint default across
Pricing kthtodefault swaps under default contagion: the matrixanalytic approach
, 2006
"... We study a model for default contagion in intensitybased credit risk and its consequences for pricing portfolio credit derivatives. The model is specified through default intensities which are assumed to be constant between defaults, but which can jump at the times of defaults. The model is transla ..."
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We study a model for default contagion in intensitybased credit risk and its consequences for pricing portfolio credit derivatives. The model is specified through default intensities which are assumed to be constant between defaults, but which can jump at the times of defaults. The model is translated into a Markov jump process which represents the default status in the credit portfolio. This makes it possible to use matrixanalytic methods to derive computationally tractable closedform expressions for singlename credit default swap spreads and k thtodefault swap spreads. We ”semicalibrate” the model for portfolios (of up to 15 obligors) against market CDS spreads and compute the corresponding k thtodefault spreads. In a numerical study based on a synthetic portfolio of 15 telecom bonds we study a number of questions: how spreads depend on the amount of default interaction; how the values of the underlying market CDSprices used for calibration influence k ththto default spreads; how a portfolio with inhomogeneous recovery rates compares with a portfolio which satisfies the standard assumption of identical recovery rates; and, finally, how well k ththto default spreads in a nonsymmetric portfolio can be approximated by spreads in a symmetric portfolio.
Credit risk and incomplete information: a nonlinear filtering approach
, 2006
"... We study reducedform portfolio credit risk models where the default intensities of the firms in a given portfolio depend on a common state variable process X. In line with market practice, we assume that this state variable process is not directly observable; instead we assume that the information ..."
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Cited by 14 (1 self)
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We study reducedform portfolio credit risk models where the default intensities of the firms in a given portfolio depend on a common state variable process X. In line with market practice, we assume that this state variable process is not directly observable; instead we assume that the information set of investors contains only the default history of the portfolio and noisy price observations of traded credit derivatives. This incompleteinformation setup is a convenient way of modelling informationdriven default contagion. In this context we study the pricing of credit derivatives and the computation of other economically interesting quantities. It turns out that this leads to a nonlinear filtering problem in a natural way. This filtering problem is studied in a general jumpdiffusion model with common jumps of the state process X and the jump process Y associated with the default times of the firms. We provide recursive updating rules for the filter and derive a finitedimensional filter for the case where X follows a finitestate Markov chain. Finally, we provide a filterapproximation result which justifies the use of the filter obtained for the finitestate Markovchain case as a computational tool for more general models.
Can standard preferences explain the prices of outofthemoney S&P 500 put options? Working Paper
, 2005
"... Prior to the stock market crash of 1987, BlackScholes implied volatilities of S&P 500 index options were relatively constant across moneyness. Since the crash, however, deep outofthemoney S&P 500 put options have become ‘expensive ’ relative to the BlackScholes benchmark. Many researche ..."
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Cited by 13 (0 self)
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Prior to the stock market crash of 1987, BlackScholes implied volatilities of S&P 500 index options were relatively constant across moneyness. Since the crash, however, deep outofthemoney S&P 500 put options have become ‘expensive ’ relative to the BlackScholes benchmark. Many researchers (e.g., Liu, Pan and Wang (2005)) have argued that such prices cannot be justified in a general equilibrium setting if the representative agent has ‘standard preferences’ and the endowment is an i.i.d. process. Below, however, we use the insight of Bansal and Yaron (2004) to demonstrate that the ‘volatility smirk ’ can be rationalized if the agent is endowed with EpsteinZin preferences and if the aggregate dividend and consumption processes are driven by a persistent stochastic growth variable that can jump. We identify a realistic calibration of the model that simultaneously matches the empirical properties of dividends, the equity premium, the prices of both atthemoney and deep outofthemoney puts, and the level of the riskfree rate. A more challenging question (that to our knowledge has not been previously investigated) is whether one can explain within a standard preference framework the stark regime change in
Modeling the recovery rate in a reduced form model. Unpublished working paper
, 2005
"... This paper provides a model for the recovery rate process in a reduced form model. After default, a firm continues to operate, and the recovery rate is determined by the value of the firm’s assets relative to its liabilities. The debt recovers a different magnitude depending upon whether or not the ..."
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Cited by 10 (2 self)
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This paper provides a model for the recovery rate process in a reduced form model. After default, a firm continues to operate, and the recovery rate is determined by the value of the firm’s assets relative to its liabilities. The debt recovers a different magnitude depending upon whether or not the firm enters insolvency and bankruptcy. Although this recovery rate process is similar to that used in a structural model, the reduced form approach is maintained by utilizing information reduction in the sense of Guo, Jarrow and Zeng (2005). Our model is able to provide analytic expressions for a firm’s default intensity, bankruptcy intensity, and zerocoupon bond prices both before and after default. KEY WORDS: credit risk, recovery rates, reduced form model, filtration reduction ∗ Helpful comments from seminar participants at Cornell University, the Johannes
Default Clustering and Valuation of Collateralized Debt Obligations”. Working Paper
, 2009
"... The recent financial turmoil has witnessed the powerful impact of the default clustering effect (i.e., one default event tends to trigger more default events in the future and crosssectionally), especially on the market of collateralized debt obligations (CDOs). We propose a model based on cumulati ..."
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The recent financial turmoil has witnessed the powerful impact of the default clustering effect (i.e., one default event tends to trigger more default events in the future and crosssectionally), especially on the market of collateralized debt obligations (CDOs). We propose a model based on cumulative default intensities that can incorporate the default clustering effect. Furthermore, the model is tractable enough to provide a direct link between singlename credit securities, such as credit default swaps (CDS), and multiname credit securities, such as CDOs. The result of calibration to the recent market data, when Bear Sterns, Lehman Brothers, etc. collapsed and default correlation among firms was substantially high, shows that the model is promising.