Related papers: How to handle negative interest rates in a CIR fra…

We consider a financial market in which the short rate is modeled by a continuous time Markov chain (CTMC) with a finite state space. In this setting, we show how to price any financial derivative whose payoff is a function of the state of…

The Dybvig-Ingersoll-Ross (DIR) theorem states that, in arbitrage-free term structure models, long-term yields and forward rates can never fall. We present a refined version of the DIR theorem, where we identify the reciprocal of the…

In this paper, we introduce a methodology based on the zero-inflated cure rate model to detect fraudsters in bank loan applications. In fact, our approach enables us to accommodate three different types of loan applicants, i.e., fraudsters,…

A new test of a wide class of interest rate models is proposed and applied to a recently developed quantum field theoretic model and the industry standard Heath-Jarrow-Morton model. This test is independent of the volatility function unlike…

For stochastic processes of non-commuting random variables we formulate a Cox-Ingersoll-Ross (CIR) stochastic differential equation in the context of free probability theory which was introduced by Voicelescu. By transforming the classical…

Inverse Optimal Control (IOC) aims to infer the underlying cost functional of an agent from observations of its expert behavior. This paper focuses on the IOC problem within the continuous-time linear quadratic regulator framework,…

We discuss a simple extension of the Ho and Lee model with generic time-dependent drift in which: 1) we compute bond prices analytically; 2) the yield curve is sensible and the asymptotic yield is positive; and 3) our analytical solution…

This paper addresses a key challenge in CDO modeling: achieving a perfect fit to market prices across all tranches using a single, consistent model. The existence of such a perfect-fit model implies the absence of arbitrage among CDO…

We consider mean-reverting CIR/CEV processes with delay and jumps used as models on the financial markets. These processes are solutions of stochastic differential equations with jumps, which have no explicit solutions. We prove the…

We present a non-parametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form.…

The interest rates (or nominal yields) can be negative, this is an unavoidable fact which has already been visible during the Great Depression (1929-39). Nowadays we can find negative rates easily by e.g. auditing. Several theoretical and…

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…

Adopting a probabilistic approach we determine the optimal dividend payout policy of a firm whose surplus process follows a controlled arithmetic Brownian motion and whose cash-flows are discounted at a stochastic dynamic rate. Dividends…

We demonstrate the effectiveness of an adaptive explicit Euler method for the approximate solution of the Cox-Ingersoll-Ross model. This relies on a class of path-bounded timestepping strategies which work by reducing the stepsize as…

Empirical evidence suggests that fixed income markets exhibit unspanned stochastic volatility (USV), that is, that one cannot fully hedge volatility risk solely using a portfolio of bonds. While [1] showed that no two-factor…

No matter the nature of the response and/or explanatory variables in a regression model, some basic issues such as the existence of an effect of the predictor on the response, or the assessment of a common shape across groups of…

We propose a modification of the classical Black-Derman-Toy (BDT) interest rate tree model, which includes the possibility of a jump with small probability at each step to a practically zero interest rate. The corresponding BDT algorithms…

The application of machine learning models can be significantly impeded by the occurrence of distributional shifts, as the assumption of homogeneity between the population of training and testing samples in machine learning and statistics…

We propose a model for the joint evolution of European inflation, the European Central Bank official interest rate and the short-term interest rate, in a stochastic, continuous time setting. We derive the valuation equation for a contingent…

We introduce a first theory of price impact in presence of an interest-rates term structure. We explain how one can formulate instantaneous and transient price impact on bonds with different maturities, including a cross price impact that…