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...

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...

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...

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 consider a tractable affine stochastic volatility model that generalizes the seminal Heston (1993) model by augmenting it with jumps in the instantaneous variance process. In this framework, we consider options written on the realized variance, and we examine the impact of the distribution of...

In this paper we investigate the asymptotics of forward-start options and the forward implied volatility smile in the Heston model as the maturity approaches zero. We prove that the forward smile for out-of-the-money options explodes and compute a closed-form high-order expansion detailing the...

We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility smile in a large class of models, including the Heston stochastic volatility and time-changed exponential Levy models.This expansion applies to both small and large maturities and...