arXiv · arXiv q-fin · 2015
The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In particular, we consider a Gaussian factor model where the short rate and the spreads are second order polynomials of Gaussian factor processes. This leads to an exponentially quadratic mod…
Zorana Grbac, Laura Meneghello, Wolfgang J. Runggaldier
arXiv · arXiv q-fin · 2015
We develop a multi-curve term structure setup in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to LIBOR swaptions data and show that a rational two-factor lognormal multi-curve model is sufficient to match market data with accuracy. We elucidate the relationship between the models developed and calibrated under a risk-neutral measure Q and their consistent equ…
Stephane Crepey, Andrea Macrina, Tuyet Mai Nguyen, David Skovmand
arXiv · arXiv q-fin · 2014
We present a HJM approach to the projection of multiple yield curves developed to capture the volatility content of historical term structures for risk management purposes. Since we observe the empirical data at daily frequency and only for a finite number of time-to-maturity buckets, we propose a modelling framework which is inherently discrete. In particular, we show how to approximate the HJM continuous time descr…
Chiara Sabelli, Michele Pioppi, Luca Sitzia, Giacomo Bormetti
arXiv · arXiv q-fin · 2024
We study the problems of consistency and of the existence of finite-dimensional realizations for multi-curve interest rate models of Heath-Jarrow-Morton type, generalizing the geometric approach developed by T. Björk and co-authors in the classical single-curve setting. We characterize when a multi-curve interest rate model is consistent with a given parameterized family of forward curves and spreads and when a model…
Claudio Fontana, Giacomo Lanaro, Agatha Murgoci
arXiv · arXiv q-fin · 2024
The financial industry has undergone a significant transition from the London Interbank Offered Rates (LIBORs) to Risk Free Rates (RFRs) such as, e.g., the Secured Overnight Financing Rate (SOFR) in the U.S. and the Cash Rate (AONIA) in Australia, as primary benchmark rates for borrowing costs. The paper examines the pricing and hedging method for financial products in a cross-currency framework with the special emph…
Yining Ding, Ruyi Liu, Marek Rutkowski
arXiv · arXiv q-fin · 2014
In the context of multi-curve modeling we consider a two-curve setup, with one curve for discounting (OIS swap curve) and one for generating future cash flows (LIBOR for a give tenor). Within this context we present an approach for the clean-valuation pricing of FRAs and CAPs (linear and nonlinear derivatives) with one of the main goals being also that of exhibiting an "adjustment factor" when passing from the one-cu…
Laura Morino, Wolfgang J. Ruggaldier
arXiv · arXiv q-fin · 2018
The general problem of asset pricing when the discount rate differs from the rate at which an asset's cash flows accrue is considered. A pricing kernel framework is used to model an economy that is segmented into distinct markets, each identified by a yield curve having its own market, credit and liquidity risk characteristics. The proposed framework precludes arbitrage within each market, while the definition of a c…
Andrea Macrina, Obeid Mahomed
arXiv · arXiv q-fin · 2016
We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or HJM modeling, can be consolidated. We model a numeraire process and multiplicative spreads between Libor rates and simply compounded OIS rates as functions of an underlying affine process. Besides allowing for ordered spreads and an exact fit to the initia…
Christa Cuchiero, Claudio Fontana, Alessandro Gnoatto
arXiv · arXiv q-fin · 2015
Collateralization with daily margining has become a new standard in the post-crisis market. Although there appeared vast literature on a so-called multi-curve framework, a complete picture of a multi-currency setup with cross-currency basis can be rarely found since our initial attempts. This work gives its extension regarding a general framework of interest rates in a fully collateralized market. It gives a new form…
Masaaki Fujii, Akihiko Takahashi
arXiv · arXiv q-fin · 2014
Historical (Stressed-) Value-at-Risk ((S)VAR), and Expected Shortfall (ES), are widely used risk measures in regulatory capital and Initial Margin, i.e. funding, computations. However, whilst the definitions of VAR and ES are unambiguous, they depend on input distributions that are data-cleaning- and Data-Model-dependent. We quantify the scale of these effects from USD CDS (2004--2014), and from USD interest rates (1…
Chris Kenyon, Andrew Green
arXiv · arXiv q-fin · 2021
Valuation adjustments, collectively named XVA, play an important role in modern derivatives pricing to take into account additional price components such as counterparty and funding risk premia. They are an exotic price component carrying a significant model risk and computational effort even for vanilla trades. We adopt an industry-standard realistic and complete XVA modelling framework, typically used by XVA tradin…
Lorenzo Silotto, Marco Scaringi, Marco Bianchetti
arXiv · arXiv q-fin · 2019
We develop a modelling framework for multiple yield curves driven by continuous-state branching processes with immigration (CBI processes). Exploiting the self-exciting behavior of CBI jump processes, this approach can reproduce the relevant empirical features of spreads between different interbank rates. In particular, we introduce multi-curve models driven by a flow of tempered alpha-stable CBI processes. Such mode…
Claudio Fontana, Alessandro Gnoatto, Guillaume Szulda
arXiv · arXiv q-fin · 2018
We construct models for the pricing and risk management of inflation-linked derivatives. The models are rational in the sense that linear 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, year-on-yea…
Henrik Dam, Andrea Macrina, David Skovmand, David Sloth
arXiv · arXiv q-fin · 2010
The crisis that affected financial markets in the last years leaded market practitioners to revise well known basic concepts like the ones of discount factors and forward rates. A single yield curve is not sufficient any longer to describe the market of interest rate products. On the other hand, using different yield curves at the same time requires a reformulation of most of the basic assumptions made in interest ra…
Andrea Pallavicini, Marco Tarenghi
arXiv · arXiv q-fin · 2010
For a long time interest-rate models were built on a single yield curve used both for discounting and forwarding. However, the crisis that has affected financial markets in the last years led market players to revise this assumption and accommodate basis-swap spreads, whose remarkable widening can no longer be neglected. In recent literature we find many proposals of multi-curve interest-rate models, whose calibratio…
Nicola Moreni, Andrea Pallavicini
arXiv · arXiv q-fin · 2020
Calibration is a highly challenging task, in particular in multiple yield curve markets. This paper is a first attempt to study the chances and challenges of the application of machine learning techniques for this. We employ Gaussian process regression, a machine learning methodology having many similarities with extended Kalman filtering - a technique which has been applied many times to interest rate markets and te…
Sandrine Gümbel, Thorsten Schmidt