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...

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...

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...

In this paper we outline the European interest rate swaption pricing formula from first principles using the Martingale Representation Theorem and the annuity measure. This leads to an expression that allows us to apply the generalized Black-Scholes result. We show that a swaption pricing...

Although the effect of interest rate stochasticity can safely be ignored for short-dated exchange traded volatility derivatives, this is not the case for the kind of long-dated OTC derivatives often used by insurance companies and other financial institutions. We therefore extend existing...

In this paper, we explore the relation between information uncertainty and S&P 500 index option returns. Since underlying state variable affecting economy is unobservable, investors have to obtain their own estimations based on available information. During such procedure, it is inevitable that...

The paper studies estimation of implied volatility and the impact of the choice of the corresponding risk-free rate proxy. We suggest to analyze the implied volatility and the risk-free rate proxy inferred in conjunction from the observed option prices. We formulate and solve an overdefined...

We consider a hybrid model for stocks and interest rates as it is proposed by GDV (Gesamtverband der Deutschen Versicherungswirtschaft) to assign market consistent values to the technical provisions of german life insurance companies. In this model, stock prices are modeled with a Black Scholes...

This is a short comment on Kung and Lee's paper. In this note, we show that the formulae given in Kung and Lee (2009) for European call and put option under Merton's model of the short rate are incorrect. We give the correct derivations making use of the "change of numeraire" technique which is...

The interest rate model by Hull and White allows to calculate an explicit formula for the price of zero bonds. From this pricing formula we deduce explicit formulas for the volatility of the instantaneous forward rate, the volatility of the interest rate (both the spot rate and interest rates of...