bluuebunny/crossref_metadata_2025_split huggingface dataset:
Kou Model
Authors: Kou Steven 
Published: May 2010

AbstractThe double exponential jump‐diffusion model (or Kou model) is an exponential Lévy model (seeExponential Lévy Models) with finite jump intensity, whose jump size distribution follows a two‐sided exponential distribution. We give an overview of properties related to the double exponential jump‐diffusion model. Certain difficulties in applying the model, such as the lack of volatility clustering, extension to multiple underlying assets, and the difficulty in distinguishing the tail behavior of asset returns, are also discussed.
Uncertain Volatility Model
Authors: Martini Claude , Jacquier Antoine 
Published: May 2010

Abstract
The everyday worry of an option trader is to make sure its profit and loss stays nonnegative.

In the framework of a delta‐hedged dynamic buy or sell strategy computed with the parameters of a complete model (like the Black–Scholes model), the P&L at maturity will in fact be zero, under the assumption that the underlying follws the model dynamic. Of course this assumption is
very
unrealistic. In a seminal paper, El Karoui, Jeanblanc and Shreve study the robustness of the B&S strategy in the context of an unknown volatility. The uncertain volatality model (UVM) setting, pioneered independently by T. Lyons and M. Avellaneda, goes one step further by finding the cheapest selling price of an option for a totally risk‐averse trader in the much more realistic setting where there is almost no information on the volatility, except that it lies in a prespecified range. Even if its concrete implementation at the level of an option portfolio is tricky, the UVM setting is a milestone in the pricing and risk management of derivatives. It also raises theoretical issues when one tries to formalize a general framework for option pricing in the context of model uncertainty.
Rating Transition Matrices
Authors: Lando David 
Published: May 2010

Abstract
Rating transition matrices play an important role in credit risk management both as a method for summarizing the empirical behavior of a rating system and as a tool for computing probabilities of rating migrations in, for example, a portfolio of risky loans. Analysis of statistical properties of rating transition matrices is intimately linked with Markov chains. Even if rating processes in general are not Markovian, statistical analysis of rating systems often focuses on assessing a particular deviation from Markovian behavior. Furthermore, the tractability of the Markovian setting can be preserved in some simple extensions.
Structural Default Risk Models
Authors: Kiesel Rüdiger , Scherer Matthias A. 
Published: May 2010

AbstractStructural‐default models rely on the appealing interpretation of corporate default as a consequence of insufficient asset values to cover contractual obligations of the corporate. Multivariate extensions typically assume correlated firm‐value processes to introduce dependence between individual default events. On a theoretical level, the resulting default correlation and portfolio‐loss distribution depend on the choice of the (multivariate) asset‐value process and the definition of the default event. In most modeling frameworks, the explicit computation of default correlations and the portfolio‐loss distribution is not possible. Therefore, balancing realistic assumptions with computational tractability is a key challenge for all multivariate structural‐default models. Especially models for large portfolios, which are required for the pricing of portfolio derivatives and risk management, use simplifying assumptions concerning the firms involved, numerical approximations, and Monte Carlo simulations for the computation of the relevant quantities. An important example is Vasicek's asymptotic single‐factor model, which under several simplifying assumptions allows the derivation of a closed‐form expression for the portfolio‐loss distribution. This formula is used to compute regulatory capital for loan portfolios under the Basel II framework.
Internal‐Ratings‐Based Approach
Authors: Pluto Katja , Tasche Dirk 
Published: May 2010

Abstract

Within the new Basel capital rules for banks (Basel II), the internal‐ratings‐based approach (IRBA) represents perhaps the most important innovation for regulatory minimum capital requirements. For the first time, subject to supervisory approval, banks are allowed to use their own risk assessments of credit exposures in order to determine the capital to be held against them. Within the IRBA, banks estimate the riskiness of each exposure on a stand‐alone basis. The risk estimates serve as input for a supervisory credit risk model (implicitly given by risk weight functions) that provides a value for capital that is deemed sufficient to cover against the credit risk of the exposure, given the assumed portfolio diversification. In order to obtain supervisory approval for the IRBA, banks must apply for IRBA and fulfill a set of minimum requirements aimed at ensuring the integrity of the rating model, rating process, and thus of the risk parameters and capital charges. Although risk quantification
via
IRBA can be of great use for the bank internal credit risk measurement and management, there are some limitations. The most important of these is surely that the IRBA provides no measure of risk concentrations. If banks are concerned about concentration effects or want to measure the diversification benefits of their portfolio, they need to develop their own, full‐fledged credit risk models.
Loan Valuation
Authors: Benzschawel Terry , Dagraca Julio , Fok Henry 
Published: May 2010

AbstractWe describe the pricing of corporate term loans and revolving credit lines within a risk‐neutral framework. The method accounts for credit‐ and market‐related term loan prepayments and for drawdown and repayment of revolving credit lines. Loans are priced using backward induction on a risk‐neutral credit‐transition lattice, testing for the prepayment criterion and default at each node. The risk‐neutral credit transitions are determined from historical data and modified to be consistent with market prices of credit default swaps. The model provides estimates of the average lives of loans and loan price and prepayments sensitivities to relevant market movements.
Credit Default Swaps
Authors: Cont Rama 
Published: May 2010

Abstract
A credit default swap (CDS) is a bilateral contract in which a protection seller compensates a protection buyer for the loss in the value of a reference security in the event of default of a reference entity. CDSs are sometimes viewed as insurance against default, but have important difference with insurance contracts. We describe the cash‐flow structure of a credit default swap, the principle behind the valuation of CDS positions, and the risk factors affecting a CDS.
Constant Maturity Credit Default Swap
Authors: Misirpashaev Timur S. 
Published: May 2010

Abstract
Constant maturity credit default swap (CM CDS) is a credit derivative with payments linked to periodic fixings of a standard CDS rate with a fixed tenor on a particular credit entity. We give references to sources describing trading conventions and strategies and summarize approaches to quantitative modeling of CM CDS, including the nonstochastic approximation, convexity adjustments, instantaneous hazard rate models, and stochastic forward spread models.
Basket Default Swaps
Authors: Overbeck Ludger 
Published: May 2010

Abstract

Basket credit derivatives are financial instruments whose payout depends on the credit behavior of a small number of credits. In this sense, they are between single‐name credit default swaps (CDS) and collateralized debt obligations (CDO)‐like structures. The standard products are
n
th‐to‐default basket in which the contingent payment is made when the
n
th default in a basket of at least
n
credits happens. Among these, first‐ or second‐to‐default swaps (FtD and StD) on a portfolio of three to five credits are most popular. As for CDOs, the benchmark valuation models are based on a copula for default times. However, some approaches based on spread models have also been developed.
Collateralized Debt Obligations (CDO)
Authors: Bruyere Richard , Jaeck Christophe 
Published: May 2010

Abstract
In the limited timeframe of a few years (2001–2007), CDOs and structured credit arguably became the hottest areas in capital markets and a crucible of financial innovation, until the 2007 subprime crisis marked the (temporary?) end of the party. This article provides a factual analysis of these developments starting from a typology of CDOs and a review of modeling techniques to an analysis of the impact of the subprime crisis on the CDO market.
CDO Square
Authors: Brasch Hans‐Jürgen 
Published: May 2010

Abstract

A CDO‐of‐CDO, or CDO square (CDO
2
), is a type of collateralized debt obligation (CDO) that has CDO tranches as reference assets. The CDO
2
market has been used for rating and capital arbitrage, repackaging, and diversification of loan and debt portfolios.
Duffie–Singleton Model
Authors: Schlögl Erik , Schlögl Lutz 
Published: May 2010

Abstract
The Duffie–Singleton model is a reduced‐form credit risk model in which instantaneous credit spreads can be identified with a “risk‐neutral mean‐loss rate due to default.” The model is driven by a set of state variables following a Markov process, and defaultable zero‐coupon bond prices are exponentially affine functions of these variables. A key assumption is the modeling of recovery in default as an exogenously given fraction of the market value of the defaultable claim. Unlike other exponentially affine model specifications, the one proposed by Duffie and Singleton is sufficiently flexible to allow default intensities (and thus credit spreads) to be negatively correlated with default‐free interest rates. The model is very tractable computationally and lends itself to econometric estimation or, alternatively, to calibration to observed market prices for purposes of relative valuation of credit derivatives.
Jarrow–Lando–Turnbull Model
Authors: Zagst Rudi , Scherer Matthias A. 
Published: May 2010

AbstractThe credit‐risk model of Jarrow, Lando, and Turnbull identifies the evolution of a firm's credit rating over time with some Markov chain. On the basis of this appealing economic interpretation, it is possible to valuate defaultable bonds and credit derivatives. The resulting prices explicitly depend on the initial rating and possible rating transitions of the reference firm in the future. The required martingale probabilities are obtained from empirical transition probabilities, which are adjusted by some risk premium.
Default Barrier Models
Authors: Gregory Jon 
Published: May 2010

Abstract
This article outlines the use of default barrier models in both single name and portfolio credit risk modeling. The economic and mathematic rationale for the modeling of default as the hitting time of a barrier is first described, followed by a description of the birth of such approaches from the classic Merton framework for pricing risky debt. The practical extensions of the Merton framework that have been used for default probability modeling and trading strategies such as capital structure arbitrage are considered. Finally the use of default barrier models in credit portfolio risk applications that require a description of credit portfolio losses is described.
Multiname Reduced Form Models
Authors: Lipton Alexander 
Published: May 2010

Abstract
In this article, we discuss single and multiname random‐intensity models. After providing a brief overview of single‐name models, we describe in some detail three popular multiname models, namely, the Duffie–Garleanu–Mortensen, Chapovsky–Rennie–Tavares, and Inglis–Lipton models. The main conclusion is that these models describe the market well, but, since they require large jumps in intensity, further work is needed if they are to be used for hedging purposes.
Local Correlation Model
Authors: Turc Julien , Herzog Benjamin 
Published: May 2010

AbstractThe local correlation model is a credit portfolio loss model that generalizes the Gaussian copula model and allows to account for the base correlation smile. The constant correlation assumption is initially relaxed within a large pool framework, which provides theoretical results used as a basis for the general model. The large pool assumption is then relaxed in order to take the portfolio's specificities into account.
Intensity Gamma Model
Authors: Joshi Mark , Stacey Alan 
Published: May 2010

Abstract
We review the intensity gamma model for pricing portfolio credit derivatives. This is a model for correlation of credit defaults based on a financially intuitive concept of business time similar to that in the variance gamma model for stock price evolution. Solving a simple equation calibrates each name to its credit spread curve. We show that the overall model can be calibrated to the market base correlation curve of a tranched collateralized debt obligation (CDO) index. Once this calibration is performed, obtaining consistent arbitrage‐free prices for nonstandard tranches, products based on different underlying names and even more exotic products such as CDO‐squared, is straightforward and rapid.
Special‐Purpose Vehicle (
SPV
)
Authors: Polizu Cristina , Jiang Jennifer 
Published: May 2010

Abstract
A special‐purpose vehicle (SPV) is a legal entity created by a firm for a specific business objective, usually in the context of securitization. SPVs are often used to finance a project or issue securities without putting at risk the original holder of the securitized portfolio. Derivative‐product companies (DPCs), structured‐investment vehicles (SIVs), and credit derivative‐product companies (CDPCs) are SPVs that operate in primarily one type of business: interest rate and foreign exchange derivatives, credit derivatives, and buy and hold assets or others. They might be exposed to credit risk, market risk, operational risk, and so on. Capital adequacy models are built to quantify the risks they are exposed to.
Structured Finance Rating Methodologies
Authors: Kocagil Ahmet E. , Papatheodorou Vasileios 
Published: May 2010

Abstract
Securitization is a mechanism by which a portfolio of financial assets such as loans, receivables, corporate debt, and other usually illiquid assets is used as a collateral for collateralized debt obligation (CDOs) or other structured finance (ABS) securities issued, typically by a special purpose vehicle (SPV), in the market. The rating agencies evaluate the different tranches of the issued securities and issue ratings in order to provide an independent opinion on the credit quality of these securities. The aim of this article is to review the ABS and CDO rating methodologies applied in the securitization market.
CDO Tranches: Impact on Economic Capital
Authors: Lee Yim T. 
Published: May 2010

AbstractCollateralization debt obligations (CDOs) are financial securities backed by a pool of assets. Claims on the underlying assets of a CDO are divided into several tranches from the riskiest to the least risky. Many financial institutions including banks are holding CDO tranches of different transactions in their credit portfolios as a result of their recent activities in CDO investing and structuring. Modeling the impact of CDO tranches on the economic capital of credit portfolios is thus becoming increasingly important. This article presents the methodology to measure the impact of CDO tranches on the economic capital and capital allocation of credit portfolios. The methodology is illustrated by presenting an example of calculating capital allocation for a synthetic CDO tranche in a credit portfolio comprised of a tranche and other loans. It is demonstrated that adding a CDO tranche to a credit portfolio increases the systematic risk of the portfolio and, consequently, a CDO tranche could require much larger economic capital compared to a loan of similar credit quality and same maturity. An important implication of our finding is that by treating a CDO tranche as a loan equivalent, only a very poor approximation of economic capital is obtained.
Eurodollar Futures and Options
Authors: Yu Yuhua 
Published: May 2010

Abstract
Eurodollar futures and the options traded on those futures are among the most widely traded interest‐rate instruments worldwide. The futures contracts are based on the three‐month interest rates earned on US dollar deposits that are held in banks located outside the United States. This article explains the contract specifications and quoting conventions of the Eurodollar products listed at the Chicago Mercantile Exchange (CME). Further, it discusses the pricing methods of these contracts.
Bond Options
Authors: Piza Marcelo 
Published: May 2010

Abstract
This article describes various types of options on bonds and presents the main approaches used for their modeling and valuation. We start with a brief description of bond option contracts and the closely related options on bond futures as well as options embedded in the bond contract itself. We then present some standard approaches for valuation restricting ourselves to options on default‐free bonds with a focus on European bond options.
We start by describing the original approaches based on the Black–Scholes–Merton model where the quantity that is directly modeled is the bond's price or yield and discuss some of the inconsistencies related to this approach. This is followed by a presentation of the Black 1976 model. We also establish a relationship between the valuation of bond options and its relation to the standard valuation approach for vanilla interest rate derivatives such as caps, floors, and swaptions. We then turn to the valuation of bond options based on a full‐term structure model focusing on the special case of short term models. We present the Jamishidian decomposition, which allows for an explicit determination of the exercise boundary for European options on coupon bonds for a class of one‐factor short‐rate models satisfying a monotonicity condition. We conclude with a brief description of the approaches used for the pricing of Bermudan and American bond options.
Constant Maturity Swap
Authors: Veilex Laurent 
Published: May 2010

AbstractThis article describes interest rate derivatives that are simple extensions of vanilla interest rate swaps: in‐arrears swaps, averaging swaps, and constant maturity swaps (CMS). Unlike vanilla swaps, these securities are sensitive to volatilityviaso‐called convexity adjustments. We demonstrate two methods for calculating convexity adjustments: the standard Black– Scholes framework and the replication method.
B
ermudan Swaptions and Callable Libor Exotics
Authors: Andersen Leif B.G. , Piterbarg Vladimir V. 
Published: May 2010

Abstract
In this article we give an overview of callable interest rate products, a product class that includes Bermudan swaptions as well as callable Libor exotics. The main contractual features of these securities are discussed and an outline of valuation algorithms is provided.
Term Structure Models
Authors: Vasicek Oldrich Alfons 
Published: May 2010

Abstract
Term structure models describe the behavior of interest rates of different maturities as a joint stochastic process. These models are a necessary tool for valuation and risk management of interest‐rate‐dependent securities.
A general theory of one‐factor term structure models was given by Vasicek. Invoking a no‐arbitrage argument, it was shown that the bond price satisfies a partial differential equation. Its solution, the bond pricing equation, is given as an expectation of the bond maturity value discounted at the short rate and adjusted for the price of risk.
A number of specific models have been developed. Vasicek gave an example of a term structure model in which the short rate follows a mean reverting random walk. Cox, Ingersoll, and Ross derived a model in which the volatility of the short rate is proportional to the square root of the short rate. Hull and White extended these two models by allowing the parameters to be time dependent, so that the model can be made consistent with initial data.
In one‐factor models, prices of interest‐rate‐contingent claims satisfy the same partial differential equation as bonds, with boundary conditions given by the claim payouts. More generally, derivatives can be valued by a change of probability measure.
Affine Models
Authors: Cuchiero Christa , Teichmann Josef , Filipovic Damir 
Published: May 2010

Abstract

Affine term structure models have gained significant attention in the finance literature, mainly due to their analytical tractability and statistical flexibility. The aim of this article is to present both theoretical foundations and empirical aspects of the affine model class. Starting from the original one‐factor short‐rate models of Vasiček and Cox
et al.
, we provide an overview of the properties of regular affine processes and explain their relationship to affine term structure models. Methods for securities pricing and for parameter estimation are also discussed, demonstrating how the analytical tractability of affine models can be exploited for practical purposes.
Swap Market Models
Authors: Galluccio Stefano , Scaillet Olivier 
Published: May 2010

Abstract

We describe the basics and fundamentals of swap market models, that is, the continuous time modeling of a set of forward swap rates on a tenor structure under different probability measures. We review the three main classes known as the
co‐terminal, co‐initial
, and
co‐sliding models
, and describe their use in interest‐rate derivative pricing. Finally, we discuss numerical implementation
via
model calibration and approximation of pricing formulae.
Markov Functional Models
Authors: Kennedy Joanne 
Published: May 2010

Abstract
Markov‐functional models can fit the observed prices of liquid instruments in a similar fashion to market models, but also have the advantage that they can be implemented as efficiently as spot‐rate models. The defining property of Markov‐functional models is that pure discount bond prices are, at any time, a function of some low‐dimensional process that is Markovian in some martingale measure and this is the key to their efficient implementation.

The driving process (or in dimension
k
> 1, a prior model based upon it) is chosen to capture the basic dynamics of the options market. The functional forms are derived numerically from market prices and the martingale properties necessary to make the model arbitrage‐free. We show how the LIBOR form of the model can be specified using the numeraire approach and the market prices of caplets. This model is qualitatively very similar to the LIBOR market model. The approach is particularly suited to formulating models appropriate for pricing callable LIBOR products such as Bermudan swaptions.
Hedging of Interest Rate Derivatives
Authors: Hyer Tom 
Published: May 2010

Abstract

Interest rate derivatives are claims based on the forward rate curve, so their hedging is best understood by studying their relation to that curve. Thus, interest rate risk is tantamount to forward rate risk; we make this definition precise and display the risk of an example swap. We explain curve build methods as a choice of mapping from observable market prices to forward rates, and define their
response functions
, which determine the instrument hedges computed with a given curve build method. We discuss real‐world methods for approximating second‐order risks. The language of response functions can be extended to volatilities in the Heath– Jarrow– Morton (HJM) picture; using this we analyze vega‐hedging methods. Finally, we discuss the complications introduced by credit and counterparty issues.