In this paper we discuss interest rate curve interpolation methods and their properties in the context of financial applications. We review the modern (multi-curve) theory of interest rate curve modeling, taking into account collateralization. Building on this solid foundation we reconsider...

We consider the valuation and risk management of derivatives on defaultable assets such as bonds taking into account funding (FVA), cash collateral, underlying default, counterparty default (CVA) and default correlation using joint default poisson process. The framework can be considered as an...

We derive representations for forward sensitivities (also known as future sensitivities) in a Monte-Carlo simulation suitable for backward and forward differentiation. We compare the performance of the two approaches.The calculation of all forward sensitivities of a Monte-Carlo simulation with n...

In this paper we present various methods for fast and accurate calculation of margin valuation adjustments (MVA). We consider the calculation of an MVA using sensitivities for the determination of the initial margin and consider the IDSA SIMM (ISDA Standard Initial Margin Model) as a...

In this note we apply the stochastic (backward) automatic differentiation to calculate stochastic forward sensitivities. A forward sensitivity is a sensitivity at a future point in time, conditional to the future states (i.e., it is a random variable). A typical application of stochastic forward...

In this paper we re-formulate the automatic differentiation (and in particular, the backward automatic differentiation, also known as adjoint automatic differentiation, AAD) for random variables. While this is just a formal re-interpretation it allows to investigate the algorithms in the...

In this paper we discuss how to incorporate analytic boundary conditions into a Monte-Carlo simulation framework and discuss their applications. The method introduced can dramatically improve the stability, robustness and accuracy of the valuation, calculation of sensitivities and stress...

In this paper we present a generic method for the Monte-Carlo pricing of (generalized) auto-callable products (aka. trigger products), i.e., products for which the payout function features a discontinuity with a (possibly) stochastic location (the trigger) and value (the payout).The Monte-Carlo...

In this paper we discuss the valuation and sensitivities of financial products with early exercise rights (e.g., Bermudan options) using a Monte-Carlo simulation. The usual way to value early exercise rights is the backward algorithm. As we will point out, the Monte-Carlo version of the backward...

In this short note we derive an exact simulation scheme for the joint distribution of (r(t),N(t)), where r denotes the short rate following a Hull-White model and $N$ denotes the numeraire.To sample the correct joint distribution of (r(t),N(t)) our scheme requires a two-factor Brownian driver....