Quantitative analysis
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
Evaluating the policy implications of the other two pillars of Basel II
This brief evaluates the supervisory-process and market-discipline pillars of the Basel II bank regulatory framework.
Optimized enterprise risk management
As the result of the increasing costs of risk and compliance activities, enterprises are beginning to integrate compliance and risk management into a comprehensive enterprise risk management function and thus proactively address all sorts of risk,…
Risk Sharing - Constructing sustainable pensions
Technical papers
Cracking VAR with kernels
Value-at-risk analysis has become a key measure of portfolio risk in recent years, but how can we calculate the contribution of some portfolio component? Eduardo Epperlein and Alan Smillie show how kernel estimators can be used to provide a fast,…
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
Loan portfolio value
Using a conditional independence framework, Oldrich Vasicek derives a useful limiting form for the portfolio loss distribution with a single systematic factor. He then derives a risk-neutral distribution suitable for traded portfolios, and shows how…
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…
Pricing with a smile
In the January 1994 issue of Risk, Bruno Dupire showed how the Black-Scholes model can be extended to make it compatible with observed market volatility smiles, allowing consistent pricing and hedging of exotic options
Modelling CDO tranches with dependent loss given default
Guido Giese presents an analytic methodology for pricing collateralised debt obligations tranches including stochastic and dependent loss given default
Dynamic asset allocation
Technical papers