Valuation Of Credit Default Swap Research Articles

Value-at-Risk and Expected Shortfall approaches for option premiums and the probability of default estimation based on ARMA models

The need to address the issue of risk management has given rise to a number of models for estimation the probability of default, as well as a special tool that allows to sell credit risk – a credit default swap (CDS). From the moment it appeared in 1994 until the crisis of 2008, that the CDS market was actively growing, and then sharply contracted. Currently, there is practically no CDS market in emerging economies (including Russia). This article is to improve the existing CDS valuation models by using discrete-time models that allow for more accurate assessment and forecasting of the selected asset dynamics, as well as new option pricing models that take into account the degree of risk acceptance by the option seller. This article is devoted to parametric discrete-time option pricing models that provide more accurate results than the traditional Black-Scholes continuous-time model. Improvement in the quality of assessment is achieved due to three factors: a more detailed consideration of the properties of the time series of the underlying asset (in particular, autocorrelation and heavy tails), the choice of the optimal number of parameters and the use of Value-at-Risk approach. As a result of the study, expressions were obtained for the premiums of European put and call options for a given level of risk under the assumption that the return on the underlying asset follows a stationary ARMA process with normal or Student's errors, as well as an expression for the credit spread under similar assumptions. The simplicity of the ARMA process underlying the model is a compromise between the complexity of model calibration and the quality of describing the dynamics of assets in the stock market. This approach allows to take into account both discreteness in asset pricing and take into account the current structure and the presence of interconnections for the time series of the asset under consideration (as opposed to the Black–Scholes model), which potentially allows better portfolio management in the stock market.

Optimal valuation of American callable credit default swaps under drawdown of Lévy insurance risk process

This paper discusses the valuation of credit default swaps, where default is announced when the reference asset price has gone below certain level from the last record maximum, also known as the high-water mark or drawdown. We assume that the protection buyer pays premium at a fixed rate when the asset price is above a pre-specified level and continuously pays whenever the price increases. This payment scheme is in favour of the buyer as she only pays the premium when the market is in good condition for the protection against financial downturn. Under this framework, we look at an embedded option which gives the issuer an opportunity to call back the contract to a new one with reduced premium payment rate and slightly lower default coverage subject to paying a certain cost. We assume that the buyer is risk neutral investor trying to maximize the expected monetary value of the option over a class of stopping time. We discuss optimal solution to the stopping problem when the source of uncertainty of the asset price is modelled by Lévy process with only downward jumps. Using recent development in excursion theory of Lévy process, the results are given explicitly in terms of scale function of the Lévy process. Furthermore, the value function of the stopping problem is shown to satisfy continuous and smooth pasting conditions regardless of regularity of the sample paths of the Lévy process. Optimality and uniqueness of the solution are established using martingale approach for drawdown process and convexity of the scale function under Esscher transform of measure. Some numerical examples are discussed to illustrate the main results.

The Valuation of Credit Default Swap with Counterparty Risk and Collateralization

This article presents a new model for valuing a credit default swap (CDS) contract that is affected by multiple credit risks of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show that a fully collateralized CDS is not equivalent to a risk-free one. In other words, full collateralization cannot eliminate counterparty risk completely in the CDS market.

A factor model for joint default probabilities. Pricing of CDS, index swaps and index tranches

A factor model is proposed for the valuation of credit default swaps, credit indices and CDO contracts. The model of default is based on the first-passage distribution of a Brownian motion time modified by a continuous time-change. Various model specifications fall under this general approach based on defining the credit-quality process as an innovative time-change of a standard Brownian motion where the volatility process is mean reverting Lévy driven OU type process. Our models are bottom-up and can account for sudden moves in the level of CDS spreads representing the so-called credit gap risk. We develop FFT computational tools for calculating the distribution of losses and we show how to apply them to several specifications of the time-changed Brownian motion. Our line of modelling is flexible enough to facilitate the derivation of analytical formulae for conditional probabilities of default and prices of credit derivatives.

Anchoring Credit Default Swap Spreads to Firm Fundamentals

In this article, we examine the extent to which firm fundamentals can explain the cross-sectional variation in credit default swap (CDS) spreads. We construct a fundamental CDS valuation by combining the Merton distance-to-default measure with a long list of firm fundamentals via a Bayesian shrinkage method. Regressing CDS quotes against the fundamental valuation cross-sectionally generates an averageR2of 77%. The explanatory power is stable over time and robust in out-of-sample tests. Deviations between market quotes and the valuation predict future market movements. The results highlight the important role played by firm fundamentals in differentiating the credit spreads of different firms.

Informed trading, heterogeneity investment, liquidity shocks and the valuation of credit default swaps

This paper explores the effect of informed trading, heterogeneity investment and liquidity shocks on the valuation of credit default swaps (CDSs). Under the condition of asymmetric information, the informed trading plays an important role in the valuation of CDS. Instruction order flow has a significant influence on CDS price. And the scope of influence changes in accordance with different time interval, company status and the size of bid-ask spread. Heterogeneity of investors seriously affects the market liquidity and subsequently affects the CDS price. The bigger heterogeneity of the investment philosophy, investment habits, investment preference and so on is the bigger risk for market liquidity, and the higher price for CDS shall be. On the contrary, the conclusion is also consistent. The effectiveness of liquidity, whether it is before or after the financial crisis, dominates the fluctuation of CDS price. The premium of liquidity accounts for 36% to 50% of the CDS price.

How Important is a Non‐Default Factor for CDS Valuation?

Unlike previous research based on structural or reduced‐form models, we investigate the importance of a non‐default factor for credit default swap (CDS) valuation by conducting non‐parametric local linear regression analyses using corporate CDS data from 2002 to 2011. We find that a model with an additional non‐default factor significantly outperforms a model with only a default factor, both in‐sample and out‐of‐sample, particularly for low credit rating CDS spreads. This improvement is robust to both credit rating and maturity. Our findings support the idea that non‐default risk is priced in CDS spreads and help explain CDS valuation. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:1088–1101, 2015

The Role and Relevance of Option Implied Volatility in Financial Markets

The research paper is an effort to review the relevance of option implied volatility in the modern day financial markets. Volatility indices such as VIX, VFTSE and India VIX act as efficient predictors of market volatility over the near term. The role implied volatility plays in providing a measure of investors fears, explaining stock returns, credit default swap valuation, measuring bank risk, and understanding interest rate models for pricing contingent claims has been emphasized. The cases of Euro dollar option markets, S&P 100 index options, agricultural commodities on New York Board of Trade, sweet crude oil futures on NYMEX have been discussed in particular.This measure of investors fear gauge is found to be superior to logit regression and Altman’s Z. It would have been helpful in predicting the UK Banking Crisis 2008. This important determinant of volatility must be incorporated in risk management strategies to lead to a robust and integrated risk management framework.

The valuation of credit default swaps including investor–counterparty–reference entity default correlation

We extend the work of Hull and White and Kettunen and Meissner and build a credit default swap (CDS) pricing model that includes default intensities and default correlation of all three involved entities, i.e., the investor (the CDS buyer), the counter-party (the CDS seller) and the underlying reference entity. We build the model in a discrete time frame, so that the user can match the timing of CDS spread payments exactly and alter cash flows if desired. We combine two octuplet trees and use swap evaluation techniques to derive a closed-form solution for the CDS spread including default correlation of all three entities. We find that the default intensity of the investor has a strong impact on the CDS spread, whereas the default correlation of the investor with other CDS entities has a minor impact. The Matlab source code of the model is provided upon request.

Unilateral counterparty risk valuation of CDS using a regime-switching intensity model

Abstract We consider the unilateral credit valuation adjustment (CVA) of a credit default swap (CDS) under a contagion model with regime-switching interacting intensities. The model assumes that the interest rate, the recovery, and the default intensities of the protection seller and the reference entity are all influenced by macro-economy described by a homogeneous Markov chain. By using the idea of “change of measure” and some formulas for the Laplace transforms of the integrated intensity processes, we derive the semi-analytical formulas for the joint distribution of the default times and the unilateral CVA of a CDS.

A Primer on Pricing and Valuation: The Case of Credit Default Swaps

Objective: To educate banks and other financial institution about the pricing and valuation of credit default swaps; to encourage banks and other financial institution, especially for those with medium size and scope to consider the beneficial use of credit default swaps with a better understanding.

The Impact of Margin Interest on the Valuationof Credit Default Swaps

These days, both exchange-traded and most OTC derivatives transactions are collateralized: The upfront payment, if any, and regular mark-to-market variation margin are held in escrow, possibly earning interest, until the contract is exercised. In theoretical modeling, interest paid on the collateral is typically ignored, under the assumption that the mark-tomarket cash flows can go either way and, in any case, the interest amounts are small. Kan and Pedersen demonstrate that this intuition is not necessarily true. For credit default swaps (CDS), the impact of margin interest can be significant; in fact, the margin interest rate should be used for discounting in calculating the fair value of CDS.

Anchoring Credit Default Swap Spreads to Firm Fundamentals

This paper examines the capability of firm fundamentals in explaining the cross-sectional variation of credit default swap (CDS) spreads. The paper constructs a fundamental-based CDS valuation by combining the Merton distance-to-default measure with a long list of firm fundamental characteristics. Regressing market CDS quotes against the fundamental valuation cross-sectionally generates an average R-squared of 77%. The cross-sectional explanatory power is stable over time, and robust in out-of-sample tests. Deviations between market quotes and the fundamental valuation predict significantly future market movements. The results highlight the important role of firm fundamentals in differentiating the credit quality of different firms.

Valuation of Credit Default Swaps with Wrong Way Risk – Model Implementation and a Computational Tune-Up

In their work, Brigo and Capponi (2010) introduce a numerical approach for calculating credit valuation adjustments (CVA) for credit default swaps (CDS). In contrast to previous research, they consider the default of the party doing the calculation, and its correlation to the defaults of the counterparty and the reference entity. Assuming bilateral counterparty credit risk, this approach generates symmetric and arbitrage free CVA. The most elaborate part of this computation is the generation of the default probability structure of the reference entity conditional on the default of either the investor or the counterparty. Brigo and Capponi (2010) suggest the use of the Fractional Fourier Transformation (FRFT) technique for this purpose. In this paper, we introduce the precise and practical algorithm for this numerical approach and display the steps needed for the FRFT technique. In addition, we offer a computational tune-up for the calculation of the conditional value of the CDS through a lognormal approximation. Throughout a variety of examples we show that this robust approximation delivers satisfying results, while requiring less computational power and less excessive implementation than the FRFT approach.

The Impact of Margin Interest on the Valuation of Credit Default Swaps

Virtually all credit default swaps (CDS) are collateralized with a daily cash settlement of the variation margin equal to the change in their mark-to-market values. We show how the interest on the variation margin (also called price alignment interest) affects the value of CDS. Specifically, we show that all CDS can be valued as the expected net present value of the premium and default contingent payments by using the same risk-neutral probability measure but different discounting rates determined by the margin interest rate (i.e., the interest rate used to compute price alignment interest) on the individual CDS. For example, if the margin interest rate is fed funds, then the discounting should be done on the overnight indexed swap (OIS) curve, and if there is no margin interest, then there should be no discounting. We show that arbitrage opportunities can occur if this valuation approach is not used. Finally, using observed market prices, we numerically demonstrate meaningful differences in CDS mark-to-mark values when the OIS curve is used for discounting instead of the customary LIBOR curve.

Valuation of Credit Default Swap with Counterparty Default Risk by Structural Model

This paper provides a methodology for valuing a credit default swap (CDS) with considering a counterparty default risk. Using a structural framework, we study the correlation of the reference entity and the counterparty through the joint distribution of them. The default event discussed in our model is associated to whether the minimum value of the companies in stochastic processes has reached their thresholds (default barriers). The joint probability of minimums of correlated Brownian motions solves the backward Kolmogorov equation, which is a two dimensional partial differential equation. A closed pricing formula is obtained. Numerical methodology, parameter analysis and calculation examples are implemented.

Single name credit default swaptions meet single sided jump models

Credit risk modeling is about modeling losses. These losses are typically coming unexpectedly and triggered by shocks. So any process modeling the stochastic nature of losses should reasonable include jumps. In this paper we review a few jump driven models for the valuation of Credit Default Swaps (CDSs) and show how under these dynamic models also pricing of (exotic) derivatives on single name CDSs is possible. More precisely, we set up fundamental firm-value models that allow for fast pricing of the ‘vanillas’ of the CDS derivative markets: payer and receiver swaptions. It turns out that the proposed model is able to produce realistic implied volatility smiles. Moreover, we detail how a CDS spread simulator can be set up under this framework and illustrate its use for the pricing of exotic derivatives with single name CDSs as underliers.

The Pricing of Credit Default Swaps under a Markov-Modulated Merton’s Structural Model

We consider the valuation of credit default swaps (CDSs) under an extended version of Merton’s structural model for a firm’s corporate liabilities. In particular, the interest rate process of a money market account, the appreciation rate, and the volatility of the firm’s value have switching dynamics governed by a finite-state Markov chain in continuous time. The states of the Markov chain are deemed to represent the states of an economy. The shift from one economic state to another may be attributed to certain factors that affect the profits or earnings of a firm; examples of such factors include changes in business conditions, corporate decisions, company operations, management strategies, macroeconomic conditions, and business cycles. In this article, the Esscher transform, which is a well-known tool in actuarial science, is employed to determine an equivalent martingale measure for the valuation problem in the incomplete market setting. Systems of coupled partial differential equations (PDEs) satisfied by the real-world and risk-neutral default probabilities are derived. The consequences for the swap rate of a CDS brought about by the regimeswitching effect of the firm’s value are investigated via a numerical example for the case of a two-state Markov chain. We perform sensitivity analyses for the real-world default probability and the swap rate when different model parameters vary. We also investigate the accuracy and efficiency of the PDE approach by comparing the numerical results from the PDE approach to those from the Monte Carlo simulation.

A model for dependent default with hyperbolic attenuation effect and valuation of credit default swap

A hyperbolic function is introduced to reflect the attenuation effect of one firm’s default to its partner. If two firms are competitors (copartners), the default intensity of one firm will decrease (increase) abruptly when the other firm defaults. As time goes on, the impact will decrease gradually until extinct. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, and the fair swap premium of a credit default swap (CDS) can be valued.

Credit Default Swap Valuation with Counterparty Risk

Using the reduced form framework with inter-dependent default correlation, we perform valuation of credit default swap with counterparty risk. The inter-dependent default risk structure between the protection buyer, protection seller and the reference entity in a credit default swap are characterized by their correlated default intensities, where the default intensity of one party increases when the default of another party occurs. We explore how settlement risk and replacement cost affect the swap rate in credit default swaps.