On cox processes and credit risky securities

Lando, David

doi:10.1007/bf01531332

Cited by 931 publications

(608 citation statements)

References 14 publications

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“…SP d (t)) is the survival probability of the counterparty (resp. the dealer) up to time t, e.g., conditional on a realization of the default intensity (or hazard rate) process in a Cox framework, see Lando (1998). Here we assume that the default times τ c and τ d are independent of the portfolio values V τ c and V τ d , respectively.…”

Section: Xvamentioning

confidence: 99%

AAD and least-square Monte Carlo: Fast Bermudan-style options and XVA Greeks

Capriotti

Jiang

Macrina

2017

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Abstract. We show how Adjoint Algorithmic Differentiation (AAD) can be used to calculate price sensitivities in regressionbased Monte Carlo methods reliably and orders of magnitude faster than with standard finite-difference approaches. We present the AAD version of the celebrated least-square algorithms of Tsitsiklis and Van Roy (2001) and Longstaff and Schwartz (2001). By discussing in detail examples of practical relevance, we demonstrate how accounting for the contributions associated with the regression functions is crucial to obtain accurate estimates of the Greeks, especially in XVA applications.

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Section: Xvamentioning

confidence: 99%

AAD and least-square Monte Carlo: Fast Bermudan-style options and XVA Greeks

Capriotti

Jiang

Macrina

2017

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“…As a time-dependent process for the trigger variable of epidemics, we here employ the so-called doubly stochastic Poisson process, or a Cox process (see [4]), which we recall briefly here.…”

Section: B Doubly Stochastic Poisson Processmentioning

confidence: 99%

Estimate on the Risk of Epidemic Outbreaks for an Insurer: A Simple Stochastic Model

Ishii¹,

Ishimura²,

Fujita³

2015

IJMO

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Abstract-Epidemics bursts have been sometimes observed in recent years, whose examples include, SARS (Severe Acute Respiratory Syndrome) and Ebola virus disease, and so on. For global companies which insure these epidemics, it is important and necessary to estimate the effect of events. Here we introduce a simple stochastic model for pricing such a kind of risks, which involves the Kermack-Mckendrick epidemic model combined with a stochastic trigger variable. The computations of our model are also given.Index Terms-Epidemic outbreaks, risk for an insurer, stochastic process, threshold theorem.

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“…A default event associated with a single firm occurs as in intensity-based models introduced by, among others, Artzner and Delbaen [1] , Madan and Unal [26], Lando [24] and Jarrow and Turnbull [21]. However our valuation mechanism incorporates information from the firm's stock price.…”

Section: General Modelmentioning

confidence: 99%

Utility valuation of multi-name credit derivatives and application to CDOs

Sircar

Zariphopoulou

2009

Quantitative Finance

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We study the impact of risk-aversion on the valuation of credit derivatives. Using the technology of utility-indifference pricing in intensity-based models of default risk, we analyze resulting yield spreads in multiname credit derivatives, particularly CDOs. We study first the idealized problem with constant intensities where solutions are essentially explicit. We also give the large portfolio asymptotics for this problem. We then analyze the case where the firms have stochastic default intensities driven by a common factor, which can be viewed as another extreme from the independent case. This involves the numerical solution of a system of reaction-diffusion PDEs. We observe that the nonlinearity of the utility-indifference valuation mechanism enhances the effective correlation between the times of the credit events of the various firms leading to non-trivial senior tranche spreads, as often seen from market data.

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On cox processes and credit risky securities

Cited by 931 publications

References 14 publications

AAD and least-square Monte Carlo: Fast Bermudan-style options and XVA Greeks

AAD and least-square Monte Carlo: Fast Bermudan-style options and XVA Greeks

Estimate on the Risk of Epidemic Outbreaks for an Insurer: A Simple Stochastic Model

Utility valuation of multi-name credit derivatives and application to CDOs

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