Related papers: Derivatives Discounting Explained
We present a new model for credit index derivatives, in the top-down approach. This model has a dynamic loss intensity process with volatility and jumps and can include counterparty risk. It handles CDS, CDO tranches, Nth-to-default and…
This article consolidates and extends past work on derivative pricing adjustments, including XVA, by providing an encapsulating representation of the adjustment between any two derivative pricing functions, within an Ito SDE/parabolic PDE…
We reconsider the valuation of barrier options by means of binomial trees from a "forward looking" prospective rather than the more conventional "backward induction" one used by standard approaches. This reformulation allows us to write…
Quantitative structuring is a rigorous framework for the design of financial products. We show how it incorporates traditional investment ideas while supporting a more accurate expression of clients' views. We touch upon adjacent topics…
In this paper we describe how to include funding and margining costs into a risk-neutral pricing framework for counterparty credit risk. We consider realistic settings and we include in our models the common market practices suggested by…
Differential ML (Huge and Savine 2020) is a technique for training neural networks to provide fast approximations to complex simulation-based models for derivatives pricing and risk management. It uses price sensitivities calculated through…
Markov decision models (MDM) used in practical applications are most often less complex than the underlying `true' MDM. The reduction of model complexity is performed for several reasons. However, it is obviously of interest to know what…
In a series of recent papers, Damiano Brigo, Andrea Pallavicini, and co-authors have shown that the value of a contract in a Credit Valuation Adjustment (CVA) setting, being the sum of the cash flows, can be represented as a solution of a…
Initial margin requirements are becoming an increasingly common feature of derivative markets. However, while the valuation of derivatives under collateralisation (Piterbarg 2010, Piterbarg2012), under counterparty risk with unsecured…
In this paper, we study the pricing of contracts in fixed income markets under volatility uncertainty in the sense of Knightian uncertainty or model uncertainty. The starting point is an arbitrage-free bond market under volatility…
The objective of the paper is to price weather contracts using temperature as the underlying process when the later follows a mean-reverting dynamics driven by a time-changed Brownian motion coupled to a Gamma Levy subordinator and…
We model the term structure of the forward default intensity and the default density by using L\'evy random fields, which allow us to consider the credit derivatives with an after-default recovery payment. As applications, we study the…
Gradient-based methods for optimisation of objectives in stochastic settings with unknown or intractable dynamics require estimators of derivatives. We derive an objective that, under automatic differentiation, produces low-variance…
The credit crisis and the ongoing European sovereign debt crisis have highlighted the native form of credit risk, namely the counterparty risk. The related Credit Valuation Adjustment, (CVA), Debt Valuation Adjustment (DVA), Liquidity…
We develop a novel framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no-arbitrage arguments, we derive the nonlinear…
A simple statement and accessible proof of a version of the Fundamental Theorem of Asset Pricing in discrete time is provided. Careful distinction is made between prices and cash flows in order to provide uniform treatment of all…
We discuss and clarify the XVA modelling framework specified in the paper "MVA by replication and regression" (Risk Magazine, May 2015) for including bilateral credit risk and funding costs in derivative pricing, and in doing so we rectify…
In this paper, we introduce a model that adds a non-linearity to discounting: the discounting factor may depend on the notional (i.e., discounted values are no longer linear in the notional). In the first part of the paper, we provide a…
This paper addresses the problem of pricing involved financial derivatives by means of advanced of deep learning techniques. More precisely, we smartly combine several sophisticated neural network-based concepts like differential machine…
We present a method to compute the derivative of a learning task with respect to a dataset. A learning task is a function from a training set to the validation error, which can be represented by a trained deep neural network (DNN). The…