We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are...

In this paper, we define and model forward risk-free term rates, which appear in the payoff definition of derivatives, and possibly cash instruments, based on the new interest-rate benchmarks that will be replacing IBORs globally. We show that the classical interest rate modeling framework can...

This paper presents a benchmarking model for validation of default probabilities of listed companies for Basel II purposes. The model is based on the recent studies on the predictive capability of structural credit risk models. Benchmark ratings and one-year default probabilities are assigned to...

This paper studies the discriminatory power and calibration quality of the structural credit risk models under the 'exogenous default boundary' approach including those proposed by Longstaff and Schwartz (1995) and Collin-Dufresne and Goldstein (2001), and 'endogenous default boundary' approach...

We present the stochastic string model of Santa-Clara and Sornette (2001), as reformulated by Bueno-Guerrero et al. (2014), as a unifying theory of the continuous-time modeling of the term structure of interest rates. We provide several new results, such as: a) an orthogonality condition for the...

In this paper, we show how the factor modeling approach widely used to model yield curve evolution in real-world applications can be adapted to pricing applications using the Musiela HJM modeling framework. The resulting risk-neutral modeling framework combines the intuitiveness and...

Risk-free rates (RFRs) play a central role in the reform of interest rate benchmarks. We study a model for RFRs driven by a general affine process. In this context, under minimal assumptions, we derive explicit valuation formulas for forward-looking and backward-looking caplets/floorlets,...

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...

The tick structure of the financial markets entails that price changes observed at very high frequency are discrete. Departing from this empirical evidence we develop a new model to describe the dynamic properties of multivariate time-series of high frequency price changes, including the high...