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This paper introduces a novel stochastic model for credit spreads. The stochastic approach leverages the diffusion of default intensities via a CIR++ model and is formulated within a risk-neutral probability space. Our research primarily…
We present a family of models for the term structure of interest rates which describe the interest rate curve as a stochastic process in a Hilbert space. We start by decomposing the deformations of the term structure into the variations of…
In 'A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options', Heston proposes a Stochastic Volatility (SV) model with constant interest rate and derives a semi-explicit valuation formula.…
We consider a jump-type Cox--Ingersoll--Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases:…
With the reform of interest rate benchmarks, interbank offered rates (IBORs) like LIBOR have been replaced by risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. and the Euro Short-Term Rate (\euro STR)…
The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible $S$ can become infectious with an infection rate $\beta$ by an…
This paper presents an axiomatic scheme for interest rate models in discrete time. We take a pricing kernel approach, which builds in the arbitrage-free property and provides a link to equilibrium economics. We require that the pricing…
In this paper we develop a framework for discretely compounding interest rates which is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the…
Pricing and hedging exotic options using local stochastic volatility models drew a serious attention within the last decade, and nowadays became almost a standard approach to this problem. In this paper we show how this framework could be…
We develop at-the-money call-price and implied volatility asymptotic expansions in time to maturity for a class of asset-price models whose log returns follow a L\'evy process. Under mild assumptions placing the driving L\'evy process in…
We consider the parametric estimation of the volatility and jump activity in a stable Cox-Ingersoll-Ross ($\alpha$-stable CIR) model driven by a standard Brownian Motion and a non-symmetric stable L\'evy process with jump activity $\alpha…
The paper is concerned with stochastic equations for the short rate process $R$ $$ dR(t)=F(R(t))dt+G(R(t-))dZ(t), $$ in the affine model of the bond prices. The equation is driven by a L\'evy martingale $Z$. It is shown that the discounted…
We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between…
In this paper, we propose a new model to address the problem of negative interest rates that preserves the analytical tractability of the original Cox-Ingersoll-Ross (CIR) model without introducing a shift to the market interest rates,…
In this paper, we present a new bivariate model for the joint description of the Bitcoin prices and the media attention to Bitcoin. Our model is based on the class of the L\'evy processes and is able to realistically reproduce the jump-type…
Traditional quantitative investment research is encountering diminishing returns alongside rising labor and time costs. To overcome these challenges, we introduce the Large Investment Model (LIM), a novel research paradigm designed to…
During the last decade Levy processes with jumps have received increasing popularity for modelling market behaviour for both derviative pricing and risk management purposes. Chan et al. (2009) introduced the use of empirical likelihood…
Recently, emerging epidemics like COVID-19 and its variants require predictive mathematical models to implement suitable responses in order to limit their negative and profound impact on society. The SIR (Susceptible-InfectedRemoved) system…
Interest rate market models, like the LIBOR market model, have the advantage that the basic model quantities are directly observable in financial markets. Inflation market models extend this approach to inflation markets, where zero-coupon…
In quantitative finance, we often model asset prices as a noisy Ito semimartingale. As this model is not identifiable, approximating by a time-changed Levy process can be useful for generative modelling. We give a new estimate of the…