Aiming to study pricing of long-dated commodity derivatives, this paper presents a class of models within the Heath, Jarrow, and Morton (1992) framework for commodity futures prices that incorporates stochastic volatility and stochastic interest rate and allows a correlation structure between...

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...

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 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...

The goal of this paper is to specify market models for credit portfolios in a top-down setting driven by time-inhomogeneous Levy processes. We provide a new framework, conditions for absence of arbitrage, explicit examples, an affine setup which includes contagion and pricing formulas for STCDOs...

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...

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...

Interest rate benchmarks are currently undergoing a major transition. The LIBOR benchmark is planned to be discontinued by the end of 2021 and 'replaced' by what ISDA calls an adjusted risk-free rate (RFR). ISDA has recently announced that the LIBOR 'replacement' will most likely be constructed...

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...