Interest rate markets
Libor's true colours
Interest rates
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
A time-homogeneous, SABR-consistent extension of the LMM
Riccardo Rebonato proposes an extension of the Libor market model (LMM) that recovers the stochastic, alpha, beta, rho (SABR) caplet prices almost exactly for all strikes and maturities. The dynamics of the volatility are chosen so as to be consistent…
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…
Smiling at convexity
The price of a constant maturity swap (CMS)-based derivative is largely determined by the value of swaption volatilities at extreme strikes. Fabio Mercurio and Andrea Pallavicini propose a simple procedure for stripping consistently implied volatilities…
Smoking adjoints: fast Monte Carlo Greeks
Monte Carlo calculation of price sensitivities for hedging is often very time-consuming. Michael Giles and Paul Glasserman develop an adjoint method to accelerate the calculation. The method is particularly effective in estimating sensitivities to a…
A difference of opinion
CMS spread options have been just about everywhere this year, with investors keen to take a view on the shape of the yield curve. But a wide variation in pricing has sparked speculation that some banks may not be modelling these products accurately. By…
A fully lognormal Libor market model
In the Gaussian Heath-Jarrow-Morton model, all discount factors are lognormal under allforward measures. The Libor market model does not have this property – only the relevantforward Libor rate is lognormal under a given forward measure. However, all…
Back to the future
Current developments in exotic interest rate products push the demand for more sophisticatedinterest rate models. Here, Jesper Andreasen presents a new class of stochastic volatility multifactoryield curve models enabling quick calibration and efficient…
Replication of flexi-swaps
Ingmar Evers and Farshid Jamshidian describe a relatively new product known as a flexi-swap and discuss its application in securitisation. A flexi-swap gives a counterparty an option to amortise the interest rate swap at an accelerated pace. They show…
Common interests
Interest rates
Excess yields in bond hedging
Litterman & Scheinkman (1991) showed that the term structure of interest rates is reliablymodelled by an affine three-factor model using principal component analysis. Such a modelis inconsistent with no arbitrage. Here, Haim Reisman and Gady Zohar derive…
Correlating market models
While swaption prices theoretically contain information on interest rate correlation, Bruce Choy, Tim Dun and Erik Schlögl argue that, for any practical purpose, this information cannot be extracted. Care must therefore be taken when pricing correlation…
Component proponents II
Christophe Pérignon and Christophe Villa propose a novel method of extracting the risk factors driving interest rates that allows both the covariance matrix of interest rates and the variances of the risk factors to vary through time. To illustrate the…
Swap vega in BGM: pitfalls and alternatives
Raoul Pietersz and Antoon PelsserPractitioners who are developing the Libor BGM model for risk management of a swap-based interest rate derivative be warned: for certain volatility functions the estimate of swap vega may be poor. This may occur for time…
Shadow interest
Using a Vasicek process for the shadow rate, Viatcheslav Gorovoi and Vadim Linetsky develop an analytical solution for pricing zero-coupon bonds using eigenfunction expansions, and show how to calibrate their model to the Japanese bond market. This…
Black smirks
Fei Zhou presents a simple stochastic volatility extension of the Black interest rate option pricing model widely used by traders. Using a perturbative expansion in volatility of volatility, he derives modified Black formulas that correctly fit the…
Volatile volatilities
When pricing exotic interest rate derivatives, calibration of model parameters to vanilla cap or swaption prices can be especially time-consuming, especially if stochastic volatility is incorporated into the standard Libor market models or low…
Calibrating Libor
With a rich spectrum of maturities and tenors to contend with, the toughest aspect of pricing interest rate options is calibrating models of forward rates to market data. Here, Damiano Brigo and Fabio Mercurio present a scheme for simultaneously…