Default times, no-arbitrage conditions and changes of probability measures

In this paper, we give a financial justification, based on no-arbitrage conditions, of the (H)-hypothesis in default time modeling. We also show how the (H)-hypothesis is affected by an equivalent change of probability measure. The main technique used here is the theory of progressive enlargements of filtration

Dynamic Defaultable Term Structure Modelling beyond the Intensity Paradigm

The two main approaches in credit risk are the structural approach pioneered in Merton (1974) and the reduced-form framework proposed in Jarrow & Turnbull (1995) and in Artzner & Delbaen (1995). The goal of this article is to provide a unified view on both approaches. This is achieved by studying reduced-form approaches under weak assumptions. In particular we do not assume the global existence of a default intensity and allow default at fixed or predictable times with positive probability, such as coupon payment dates. In this generalized framework we study dynamic term structures prone to default risk following the forward-rate approach proposed in Heath-Jarrow-Morton (1992). It turns out, that previously considered models lead to arbitrage possibilities when default may happen at a predictable time with positive probability. A suitable generalization of the forward-rate approach contains an additional stochastic integral with atoms at predictable times and necessary and sufficient conditions for a suitable no-arbitrage condition (NAFL) are given. In the view of efficient implementations we develop a new class of affine models which do not satisfy the standard assumption of stochastic continuity. The chosen approach is intimately related to the theory of enlargement of filtrations, to which we provide a small example by means of filtering theory where the Azema supermartingale contains upward and downward jumps, both at predictable and totally inaccessible stopping times

Pricing Currency Risk: Facts and Puzzles from Currency Boards

Hard pegs, such as currency boards, intend to reduce or even eliminate currency risk. This paper investigates the patterns and determinants of the currency risk premium in two currency boards -- Argentina and Hong Kong. Despite the presumed rigidity of currency boards, the currency premium is almost always positive and at times very large. Its term structure is usually upward sloping, but flattens out or even becomes inverted at times of turbulence. Currency premia differ across markets. The forward discount typically exceeds the currency premium derived from interbank rates, particularly during crisis times. The large magnitude of these cross-market differences can be the consequence of unexploited arbitrage opportunities, market segmentation, or other risks embedded in typical measures of currency risk. The premium and its term structure depend on domestic and global factors, related to devaluation expectations and risk perceptions.

Pricing currency risk : facts and puzzles from currency boards

The authors investigate the patterns and determinants of the currency risk premium in two currency boards-Argentina and Hong Kong. Despite the presumed rigidity of currency boards, currency premium is almost always positive and at times very large. Its term structure is usually upward sloping, but flattens out or even becomes inverted at times of turbulence. Currency premia differ across markets. The forward discount typically exceeds the currency premium derived from interbank rates, particularly during times of crisis. The large magnitude of these cross-market differences can be the consequence of unexploited arbitrage opportunities, market segmentation, or other risks embedded in typical measures of currency risk. The premium and its term structure depend on domestic and global factors related to devaluation expectations and risk perceptions.Environmental Economics&Policies,Fiscal&Monetary Policy,Economic Theory&Research,Banks&Banking Reform,Payment Systems&Infrastructure,Environmental Economics&Policies,Fiscal&Monetary Policy,Economic Theory&Research,Macroeconomic Management,Banks&Banking Reform

A unified approach to pricing and risk management of equity and credit risk

We propose a unified framework for equity and credit risk modeling, where the default time is a doubly stochastic random time with intensity driven by an underlying affine factor process. This approach allows for flexible interactions between the defaultable stock price, its stochastic volatility and the default intensity, while maintaining full analytical tractability. We characterize all risk-neutral measures which preserve the affine structure of the model and show that risk management as well as pricing problems can be dealt with efficiently by shifting to suitable survival measures. As an example, we consider a jump- to-default extension of the Heston stochastic volatility model

Systematic risk of CDOs and CDO arbitrage

“Arbitrage CDOs” have recorded an explosive growth during the years before the outbreak of the financial crisis. In the present paper we discuss potential sources of such arbitrage opportunities, in particular arbitrage gains due to mispricing. For this purpose we examine the risk profiles of Collateralized Debt Obligations (CDOs) in some detail. The analyses reveal significant differences in the risk profile between CDO tranches and corporate bonds, in particular concerning the considerably increased sensitivity to systematic risks. This has farreaching consequences for risk management, pricing and regulatory capital requirements. A simple analytical valuation model based on the CAPM and the single-factor Merton model is used in order to keep the model framework simple. Then, the conditional expected loss curve (EL profile) is studied in some detail. In the next step, the asset correlation associated with a CDO tranche is estimated treating the structured instrument as a single-name credit instrument (i.e., a loan equivalent). While tractable, the loan-equivalent approach requires appropriate parameterization to achieve a reasonable approximation of the tranche´s risk profile. We consider the tranche as a “virtual” borrower or bond for which a single-factor model holds. Then, the correlation parameter is calculated via a non-linear optimization. This “bond representation” allows to approximate the risk profile (expressed by the EL profile) using a single-factor model and to express the dependence on the systematic risk factor via the corresponding asset correlation. It turns out that the resulting asset correlation is many times higher than that of straight bonds. Then, the Merton type valuation model for the corresponding bond representations is applied for valuation of the CDO tranches. Using a sample CDO portfolio, some opportunities for “CDO arbitrage” are described where it is assumed that investors are guided solely by the tranches’ rating and ignore the increased systematic risk for pricing. In the next section we discuss how tranches with high systematic risk can be generated and how CDO arrangers can exploit this to their advantage. It comes as no surprise that precisely these types of structures featured in many of the CDOs issued prior to the outbreak of the financial crisis. --Collateralized debt obligations (CDO),arbitrage CDOs,credit rating,expected loss profile,bond representation,systematic risk of CDO tranches,CDO pricing