Multiscale Intensity Models for Single Name Credit Derivatives

Regular and singular perturbation expansions are given for the electrostatic potential of a uniformly charged dielectric sphere in a 1-1 electrolyte for distances the order of the sphere radius and for much larger distances the order of a Debye length. Since the regular perturbation expansion valid near the sphere diverges as R and the comparable singular perturbation expansion as In R, we match the regular perturbation expansions at small and large distances. The matched perturbation expansions hold for potentials somewhat greater than 25 mv and are a nonlinear generalization of the expansion of Gronwall et al.

Option Valuation Using Asymptotic Expansion

This paper mainly discusses the pricing of credit default swap (CDS) in the fractional dimension environment. We assume that the default intensity of a firm depends on the default states of counterparty firms and the term structure of interest rates, but the contagious impact of the counterparty firm is decreasing over time, until disappears. The interest rate risk is reflected by the fractional Vasicek interest rate model. We model the firm’s default intensity in the looping default framework and derive the pricing formulas of risky bonds and credit default swap.

In this study, we extend the multiscale stochastic volatility model of [Fouque J‐P, Lorig MJ, SIAM J Financial Math. 2011;2(1):221‐254] by incorporating a slow varying factor of volatility. The resulting model can be viewed as a multifactor extension of the Heston model with two additional factors driving the volatility levels. An asymptotic analysis consisting of singular and regular perturbation expansions is developed to obtain an approximation to European option prices. We also find explicit expressions for some essential functions that are available only in integral formulas in the work of [Fouque J‐P, Lorig MJ, SIAM J Financial Math. 2011;2(1):221‐254]. This finding basically leads to considerable reduction in computational time for numerical calculation as well as calibration problems. An accuracy result of the asymptotic approximation is also provided. For numerical illustration, the multifactor Heston model is calibrated to index options on the market, and we find that the resulting implied volatility surfaces fit the market data better than those produced by the multiscale stochastic volatility model of [Fouque J‐P, Lorig MJ, SIAM J Financial Math. 2011;2(1):221‐254], particularly for long‐maturity call options.

On Pricing Credit Default Swaps with Observable Covariates

This article provides a new approach to modeling dependent defaults in a portfolio. Our top-down approach involves modeling the defaults of a set of firms and then allocating the aggregate default risk in each set to the individual firms in the set. The major advantage of our approach is that we can easily incorporate economic factors that lead to high correlations in default intensities. Once we obtain a measure of default risk for a set of firms we apply a process called random thinning to characterize the default intensity of a single firm that is a member of the set. Each firm is assigned a portion of its set9s default risk based on firm characteristics such as leverage, asset volatility, and asset correlation. This allows both pricing of portfolios and single name credits with the ease of a reduced form model and the economic motivation of a structural model. Furthermore, we do comparative static exercises to show how the model behaves and we conduct simulations to compare it to the reduced form and structural models9 predictions of single and multi-name credit derivative prices. <b>TOPICS:</b>Accounting and ratio analysis, credit default swaps, simulations

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

Valuing portfolio credit derivatives, such as CDO tranches based on a broad portfolio of credits, like the CDX.NA.IG index portfolio with 125 investment grade names, remains a very difficult problem. Only approximate and imperfect solutions are available so far. The industry standard Gaussian copula model has several known shortcomings, including the fact that it is a static model which does not offer a clear way to tie together valuation for CDO tranches with different maturities, and it doesn9t generate wide enough spreads to match market prices for the supersenior tranches. Efforts to make the default hazard rate dynamic by modeling it as a diffusion run into the second difficulty when the models are calibrated to market prices. This article introduces a dynamic process for the cumulative hazard rate for a credit portfolio, that allows discrete jumps with jump size increasing in the number of jumps. This approach ties together the market quotes for CDO tranches of different maturities into a unified valuation framework. It also can generate large enough default intensity once several defaults have occurred to produce default risk on the senior and supersenior tranches of the magnitude that the market seems to be incorporating into their prices. <b>TOPICS:</b>Credit default swaps, factor-based models, CLOs, CDOs, and other structured credit

Abstract. The objective of this article is theoretical and methodological justifying of determining algorithm of the cost of debt capital for enterprises functioning in emerging markets (EM). The methods of research: analysis and synthesis, system analysis, comparative analysis, empirical and statistical methods, factor analysis. Results. In this article key determinants of interest rates on debt capital for enterprises and their impact on the procedure of discount rate calculation are determined. The issue of the cost of debt calculation of enterprises in condition of absence of complete information concerning systematic and non-systematic crediting risks is studied. Differences between interest rate on the loan fixed in credit agreement and expected by creditors the cost of debt are identified. It is determined that the key factor impacting the deviation level of market value of debt capital from the nominal, and respectively, deviation of the cost of debt from the cost of capital is probability of default (PD). At the minimum values of PD, the contract interest rate corresponds to the rate of cost of debt and it is advisable to use it for discount rate calculation. Critical analysis of alternative methodological approaches of the cost of debt calculation is made. Ways of integrating of market information concerning credit default swaps into the process of expected cost of debt calculation are justified. Factors of shadowing of rates of the cost of debt and ways of reducing of shadow transactions’ level in the credit market are identified. Conclusions. At high PD values, expected by market premium for default risk may exceed the contract interest rate, which necessitates constant monitoring of credit risks and appropriate adaptation of interest rates. In the paper the algorithm of such adaptation are proposed. It is shown that in the case of non-use of interest rates adjustment taking into account changes in PD, CDS and LGD, premium for creditors’ systematic risk can differ significantly from market values of similar enterprises (peer-group), and estimated value of the cost of debt can acquire negative values. Contract (promised) interest rate should be set in such way that the premium for systematic risk of providing debt capital will be at the level of similar companies and does not change significantly as a result of probability of default changes. If in practice the opposite situation occurs, it is the evidence of contract interest rate shadowing, absence of effective system of assessment and management of credit risks. For solving the problem of interest rate transparency and filling of information gaps concerning PD borrowers in EM countries, should intensify CDS market. Keywords: debt capital, default probability, non-performing loans, credit default swap, credit spread, debt capital premium, shadow economy. JEL Classification E47 Formulas: 16; fig.: 0; tabl.: 3; bibl.: 15.

Credit risk pricing is perhaps an understudied topic in comparisons to its profound impact on the world’s financial markets and economies. This study uses established price discovery techniques to develop a method of price discovery for credit risk in three financial markets: equity, debt, and credit derivative. This chapter is motivated by the development of credit-related instruments and signals of stock price movements of South-Eastern European countries—Bulgaria, Croatia, Greece, Hungary, Romania, Slovenia, Slovakia, and Turkey—during the recent financial crisis. In this study, the authors evaluate the dynamics of fiscal risk or country risk measured by sovereign Credit Default Swap (CDS), liquidity risk measured bond markets, and stock markets for the monthly based September 2008 – February 2011 period. The study examines monthly data observing 38 months and 8 countries. A panel vector autoregression model is proposed for changes in Long-Term Interest Rate (LTIR), changes in CDS spreads (CDS), and changes in stock index. In conclusion, CDS markets and stock markets are more significant than bond markets in explaining the post-crisis relationship among developing South-Eastern European countries. The analysis displays that long-term monetary policy did not affect CDS premium and stock index level. A strong relationship is found between the CDS spread and stock market. During financial crisis and after the crisis, the correlations among CDS, stock, and bond markets are collapsed by panicked investors’ rapid movement and wild speculators. This risk perception can explain the difference between the finance theory and practices in the market.

PurposeThe purpose of this paper is to explain the rule recently published by the US Commodity Futures Trading Commission that establishes a timetable for the mandatory clearing of interest rate and credit default swaps through a clearinghouse.Design/methodology/approachThe paper discusses the structure of cleared trades in swaps, the classes of interest rate and credit default swaps that are subject to mandatory clearing under the CFTC's new rule and the affirmative and negative specifications for each class, the phased approach adopted by the CFTC for the mandatory clearing compliance schedule, and the end‐user and inter‐affiliate exemptions from the mandatory clearing requirement.Findings“Centralized clearing,” a process in which bilaterally negotiated trades of derivatives have to be given up to a centralized clearinghouse, is a cornerstone of the new global regulatory system for derivatives. Its proponents argue that centralized clearing will help to mitigate systemic risk by helping counterparties identify and net positions. The paper outlines the clearing rules in the USA for interest rate and credit default swaps.Originality/valueThe paper provides expert guidance from experienced financial services lawyers.

The major sources of credit risk are default probability and recovery. Together with interest rate risk, they determine the price of credit derivatives. In this article, we study the relative importance of these sources by testing pair-nested structural models with data from credit default swaps. By comparing pairs of models that are nested in terms of their assumptions about these sources (one model is a special case, or restriction, of the other), we are able to understand what causes a pricing model to succeed or fail. Using credit default swap data from 2/15/2000 through 4/8/2003, we find that random interest rates and random (asset value) recovery are important assumptions for achieving accurate pricing, while continuous default times (as opposed to a single default time) is not. <b>TOPICS:</b>Risk management, credit risk management

This article describes a continuous-time Markov approach to the riskneutral pricing of a credit default swap with counterparty risk. The key parameters in the approach are the transition rates, which naturally incorporate the ideas of contagion. Correlation (which is time-dependent) is a derived quantity, which results from contagion. An expansion in powers of a small parameter (a risk-neutral default probability) allows analytic formulae to be obtained for all relevant quantities. Thus, the problem of the calibration of the model to the market prices of the bonds of the reference entity and the counterparty, as well as to the credit default swap spreads of the reference entity (which are independent of the bond spreads in the case of counterparty risk), is solved. This is done with the help of analytic results for the spread of a credit default swap with counterparty risk, as well as for other derivative prices. A comparison with results produced by the market-standard Gaussian copula approach indicates that the market-standard approach could be significantly improved by allowing the copula correlation coefficient to be time-dependent.

Abstract/Zusammenfassung The spread risk premium component of credit default swap (CDS) spreads represents a compensation demanded by protection sellers for future changes in CDS spreads caused by unpredictable fluctuations in the reference entity’s risk-neutral default intensity. This paper defines and estimates a measure of the spread risk premium component in CDS spreads of a sample of European investment-grade firms by using a stochastic intensity credit model. Our results show that, on average, investors demand a positive premium for such mark-to-market risks. After controlling for CDS market conditions, like liquidity and supply/demand effects, a panel data analysis of the estimated spread risk premia reveals a positive impact of event risk captured by the overall stock market volatility and a negative impact of investors’ appetite for exposure to credit markets as reflected by the overall CDS market. Marktrisikopr mien in Credit Default Swaps von Unternehmen Die Marktrisikopramie im Credit Default ...

Credit Derivative Theory &amp; Practice A Credit Primer &amp; Review of the Impact of ISDA Standardization on Credit Default Swap Pricing &amp; Credit Model Calibration