Risk magazine/Technical paper
A telling scope
The number of technical articles submitted each year to Risk has stabilised at around 90, and a high proportion of them are still about credit derivatives and credit portfolio risk analysis. In fact, in our Cutting Edge pages and behind the scenes we…
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
Kalibrierung - Markov-Projektion zur Kalibrierung der Volatilität
Der Neueste Stand
Expected shortfall - una coda in due parti
APPROFONDIMENTI. RISCHIO DEL PORTAFOGLIO CREDITI
Risk contributions from generic user-defined factors
In this article, Attilio Meucci draws on regression analysis to decompose volatility, value-at-risk and expected shortfall into arbitrary combinations or aggregations of risk factors, and presents a simple recipe to implement this approach in practice
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
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
Calibration of CDO tranches with the dynamical GPL model
Consistent calibration of a credit index and its tranches across maturities with a single arbitrage-free model is a difficult problem. Here, Damiano Brigo, Andrea Pallavicini and Roberto Torresetti show that a simple loss dynamics based on the…
Realised volatility and variance: options via swaps
Volatility Options
Credit risk contagion
In a recession, company defaults increase due to both the worsening economic environment and the specific links between customers and suppliers. Banks intuitively know that customer default can cause supplier default. Duncan Martin and Chris Marrison…
Markovian projection for volatility calibration
Vladimir Piterbarg looks at the 'Markovian projection method', a way of obtaining closed-form approximations of European-style option prices on various underlyings that, in principle, is applicable to any (diffusive) model. The aim is to distil the…
The vanna-volga method for implied volatilities
Cutting Edge - Option pricing
Default and recovery correlations - a dynamic econometric approach
Integrating coherences between defaults and loss given default (LGD) is postulated by Basel II. If there is a positive correlation between the two, separate models for each lead to biased estimates for the LGD parameters, and the economic loss is…
Variance swaps under no conditions
Conditional variance swaps are claims on realised variance that is accumulated when the underlying asset price stays within a certain range. Being highly sensitive to movements in both asset price and its variance, they require a very reliable model for…
Valuing inflation futures contracts
In recent years, futures contracts written on inflation (specifically, on the ratio of the consumer price index (CPI) level at two different times) have been introduced. Working within the Jarrow & Yildirim (2003) model, John Crosby derives formulas for…
The intrinsic currency valuation framework
Introducing the concept of the intrinsic value of a currency, Paul Doust shows how to use foreign exchange market volatilities to calculate the volatilities of intrinsic currency values and the correlations between them
When did the JGB market become efficient?
Focusing on the deviation from the fair-yield curve, Koichi Miyazaki and Satoshi Nomura discuss the transition in efficiency observed in the Japanese government bond market and find out that the turning point was in 1996, when the Japanese repo market…
Shortfall: a tail of two parts
Richard Martin and Dirk Tasche show that the expected shortfall, when used in the conditional independence framework, has an elegant decomposition into systematic (risk-factor-driven) and unsystematic parts. The theory is compared and contrasted with the…
Default and recovery correlations - a dynamic econometric approach
Integrating coherences between defaults and loss given default (LGD) is postulated by Basel II. If there is a positive correlation between the two, separate models for each lead to biased estimates for the LGD parameters, and the economic loss is…
The vanna-volga method for implied volatilities
Option pricing
Der indirekte Blick aus dem Sattel
Der Neueste Stand. Kreditportfoliorisiken
Sorridere alle convessità
Approfondimenti. Volatilità implicita