Quantitative analysis
The contractual trust arrangement
Technical papers
Assets relative risk for long-term investors
Technical papers
The probability approach to default probabilities
Default estimation for low-default portfolios has attracted attention as banks contemplate the requirements of Basel II's internal ratings-based rules. Here, Nicholas Kiefer applies the probability approach to uncertainty and modelling to default…
Market-implied Archimedean copulas
Computations of implied copulas are a central element in producing loss distributions of bespoke portfolios and pricing their tranches. This process is made feasible by the availability of index tranche pricing data. Luigi Vacca shows how it is possible…
Uncovering PD/LGD liaisons
Francisco Sanchez, Roland Ordovas, Elena Martinez and Manuel Vega consider the presence of correlation between default and recovery through the familiar variance of loss formula. Business cycle dependence permits a neat decomposition of the variance…
Combining the SABR and LMM models
Pierre Henry-Labordere analyses a stochastic volatility Libor market model that combines the SABR and Brace-Gatarek-Musiela (BGM) models in a natural way
Guaranteed links to the life market
Technical papers
Factor models for credit correlation
Stewart Inglis and Alex Lipton describe dynamic and static factor models for credit correlation, and show how the static model can be calibrated to the market and used for the pricing of standard and bespoke tranches including tranchelets
Taking stock of Pillar II
Technical papers
Managing interest rate risk for non-maturity deposits
Marije Elkenbracht and Bert-Jan Nauta introduce two dynamic hedge strategies to stabilise the margin between investment return and client coupon. As extensions of Jarrow & van Deventer's model, these strategies can be used for both interest rate risk…
Gamma process dynamic modelling of credit
The existing generation of credit derivatives models is unsatisfactory because they generally contain arbitrage, cannot describe the dynamics of the process, and are hard to extend beyond vanilla products. Martin Baxter has created a new tractable family…
A time-homogeneous, SABR-consistent extension of the LMM
Riccardo Rebonato proposes an extension of the Libor market model (LMM) that recovers the SABR caplet prices almost exactly for all strikes and maturities. The dynamics of the volatility are chosen so as to be consistent across expiries, to be…
Calibration of PD term structures: to be Markov or not to be
A common discussion in credit risk modelling is the question of whether term structures of default probabilities can be satisfactorily modelled by Markov chain techniques. Christian Bluhm and Ludger Overbeck show that empirical multi-year default…
Hedging for the duration
As spreads to be earned on other fixed income products have declined, mortgages have become more attractive but investors should know what risks are hedged and why. Mark Raaberg considers the main risk dynamics of hedging mortgages and why duration is a…
The true cost of no-cost mortgages
Banks offering no-cost mortgages have been accused of hiding the real cost of the loan from borrowers. But as Andrew Kalotay and Jinghua Qian explain, lenders can also run into problems if they fail to calculate correctly the prepayment behaviour of…
Dynamic optimisation for investors
Technical papers
Modelling inflation
Lars Kjaergaard models inflation using a three-factor Gaussian method. This gives a simple description of derivatives linked to inflation and interest rates, and allows for fast evaluation. He then shows how the model can be calibrated
Calibrating and pricing with local volatility models
Cutting edge - Option pricing
Gamma process dynamic modelling of credit
The existing generation of credit derivatives models is unsatisfactory because they generally contain arbitrage, cannot describe the dynamics of the process, and are hard to extend beyond vanilla products. Martin Baxter has created a new tractable family…
Pricing basis risk in survivor swaps
Technical papers
The determinants of corporate credit spreads
Credit default swaps (CDSs) are an integral tool used for the management of credit risk by financial institutions. Despite their importance, good models for the determination of CDS spreads, also called corporate credit spreads, are not readily available…
Calibrating and pricing with embedded local volatility models
Consistently fitting vanilla option surfaces when pricing volatility derivatives such as Vix options or interest rate/equity hybrids is an important issue. Here, Yong Ren, Dilip Madan and Michael Qian Qian show how this can be accomplished, using a…
Going downturn
There is much debate regarding the definition of 'downturn' loss given default (LGD). In this article, Michael Barco offers an analytic approach for calculating downturn LGD so that credit risk capital is not underestimated or overestimated