David Skovmand

Affine LIBOR models with multiple curves: theory, examples and calibration

We introduce a multiple curve framework that combines tractable dynamics and semianalytic pricing formulas with positive interest rates and basis spreads. Negative rates and positive spreads can also be accommodated in this framework. The dynamics of overnight indexed swap and LIBOR rates are specified following the methodology of the affine LIBOR models and are driven by the wide and flexible class of affine processes. The affine property is preserved under forward measures, which allows us to derive Fourier pricing formulas for caps, swaptions, and basis swaptions. A model specification with dependent LIBOR rates is developed that allows for an efficient and accurate calibration to a system of caplet prices.

Overpricing and Hidden Costs of Structured Products for Retail Investors: Evidence from the Danish Market for Principal Protected Notes

This paper studies the cost structure and pricing efficiency of principal protected notes (PPNs) from the Danish retail market. Our data set consists of detailed information on almost 400 Danish issues of PPNs during the period from 1998 to 2009. Comparing actual offer prices with theoretical fair values we find that on average PPNs are overpriced by about 6%. While overpricing of structured retail products is well-documented in the literature, our paper is the first to compare the level of overpricing with the product costs disclosed by sellers at issuance. We find that on average only about half of the overpricing can be explained by disclosed product costs. The finding of a significant hidden cost component in structured retail products is new to the literature. At the individual instrument level we find time to maturity and indicators of product complexity to be important determinants of costs and of the degree of overpricing, but other factors such as arranger and issuer size play a part as well. The degree of overpricing of PPNs has declined over time, but the unexplained cost component - hidden costs - has not.

Rational Models for Inflation-Linked Derivatives

We construct models for the pricing and risk management of inflation-linked derivatives. The model is rational in the sense that affine payoffs written on the consumer price index have prices that are rational functions of the state variables. The nominal pricing kernel is constructed in a multiplicative manner that allows for closed-form pricing of vanilla inflation products suchlike zero-coupon swaps, caps and floors, year-on-year swaps, caps and floors, and the exotic limited price index swap. The model retains the attractive features of a nominal multi-curve interest rate model such as closed-form pricing of nominal swaptions. We conclude with examples of how the model can be calibrated to EUR data.

Numerical methods for the Lévy LIBOR model

The aim of this work is to provide fast and accurate approximation schemes for the Monte Carlo pricing of derivatives in the Levy LIBOR model of Eberlein and Ozkan [4]. Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods are generally slow. We propose an alternative approximation scheme based on Picard approximations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is evolved independently of the other rates in the term structure. This enables simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.