We derive valuation formulas for caps and floors on backward-looking term rates in the Black-1976, Bachelier and Hull-White-1-Factor models explicitly regarding valuation in the fixing period, extending and detailing results of [Lyashenko & Mercurio 2019, Henrard 2019, Turfus 2020]. These...

In this paper, we introduce an extension to the LIBOR Market model that is suitable to incorporate both sudden market shocks as well as changes in the overall economic climate into the interest rate dynamics. This is achieved by substituting the simple diffusion process of the original LIBOR...

We study the term structure of the implied volatility in a situation where the smile is symmetric. Starting from the result by Tehranchi that a symmetric smile generated by a continuous martingale necessarily comes from a mixture of normal distributions, we derive representation formulae for the...

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...

SABR stochastic volatility model is appealing for modeling smile and skew of option prices. Hagan, who first proposed this model, derived a closed form approximation for european options and showed that it provides consistent and stable hedges. Here I prove a new exact closed formula for the...

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...

Does modelling stochastic interest rates, beyond stochastic volatility, improve pricing performanceon long-dated commodity derivatives? To answer this question, we consider futuresprice models for commodity derivatives that allow for stochastic volatility and stochastic interestrates and a...

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...

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...

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...