Related papers: Multi-curve HJM modelling for risk management
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…
We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads…
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…
This manuscript introduces deep learning models that simultaneously describe the dynamics of several yield curves. We aim to learn the dependence structure among the different yield curves induced by the globalization of financial markets…
We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in…
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…
In energy markets, joint historical and implied calibration is of paramount importance for practitioners, yet notoriously challenging due to the need to align historical correlations of futures contracts with implied volatility smiles from…
We provide a general HJM framework for forward contracts written on abstract market indices with arbitrary fixing and payment adjustments, and featuring collateralization in any currency denominations. In view of this, we first provide a…
We propose Variational Heteroscedastic Volatility Model (VHVM) -- an end-to-end neural network architecture capable of modelling heteroscedastic behaviour in multivariate financial time series. VHVM leverages recent advances in several…
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…
Stochastic volatility models are the backbone of financial engineering. We study both continuous time diffusions as well as discrete time models. We propose two novel approaches to estimating stochastic volatility diffusions, one using…
Local Volatility (LV) is a powerful tool for market modeling, enabling the generation of arbitrage-free scenarios calibrated to all European options. To implement LV, we need to interpolate and extrapolate option prices. This approach is…
The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for…
We statistically analyse a multivariate HJM diffusion model with stochastic volatility. The volatility process of the first factor is left totally unspecified while the volatility of the second factor is the product of an unknown process…
We develop a unified framework for modeling multiple term structures arising in financial, insurance, and energy markets, adopting an extended Heath-Jarrow-Morton (HJM) approach under the real-world probability. We study market viability…
We consider discrete time Heath-Jarrow-Morton type interest rate models, where the interest rate curves are driven by a geometric spatial autoregression field. Strong consistency and asymptotic normality of the maximum likelihood estimators…
A new modelling approach that directly prescribes dynamics to the term structure of VIX futures is proposed in this paper. The approach is motivated by the tractability enjoyed by models that directly prescribe dynamics to the VIX,…
In academic literature portfolio risk management and hedging are often versed in the language of stochastic control and Hamilton--Jacobi--Bellman~(HJB) equations in continuous time. In practice the continuous-time framework of stochastic…
This article studies a portfolio optimization problem, where the market consisting of several stocks is modeled by a multi-dimensional jump-diffusion process with age-dependent semi-Markov modulated coefficients. We study risk sensitive…
We introduce the Historical and Dynamic Volatility Ratios (HVR/DVR) and show that equity and index volatilities are cointegrated at intraday and daily horizons. This allows us to construct a VECM to forecast portfolio volatility by…