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In the standard Black-Scholes-Merton framework, dividends are represented as a continuous dividend yield and the pricing of Vanilla options on a stock is achieved through the well-known Black-Scholes formula. In reality however, stocks pay…
Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. We propose a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
Traditionally, data valuation (DV) is posed as a problem of equitably splitting the validation performance of a learning algorithm among the training data. As a result, the calculated data values depend on many design choices of the…
We propose a new forward-backward stochastic differential equation solver for high-dimensional derivatives pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo…
A key driver of Credit Value Adjustment (CVA) is the possible dependency between exposure and counterparty credit risk, known as Wrong-Way Risk (WWR). At this time, addressing WWR in a both sound and tractable way remains challenging:…
We consider pricing weather derivatives for use as protection against weather extremes. The method described utilizes results from spatial statistics and extreme value theory to first model extremes in the weather as a max-stable process,…
The vector cost bimatrix game is a method for multi-objective decision making that enables autonomous robotic systems to optimize for multiple goals at once while avoiding worst-case scenarios in neglected objectives. We expand this…
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…
Credit Valuation Adjustment is a balance sheet item which is nowadays subject to active risk management by specialized traders. However, one of the most important risk factors, which is the vector of default intensities of the counterparty,…
We consider the problem of pricing American Exchange options driven by a L\'evy process. We study the properties of American Exchange options, we represented it as the sum of the price of the corresponding European exchange option price and…
We consider the problem of pricing perpetual American options written on dividend-paying assets whose price dynamics follow a multidimensional Black and Scholes model. For convex Lipschitz continuous reward functions, we give a…
This article presents fast lower and upper estimates for a large class of options: the class of constrained multiple exercise American options. Typical options in this class are swing options with volume and timing constraints, and passport…
Shapley value attribution (SVA) is an increasingly popular explainable AI (XAI) method, which quantifies the contribution of each feature to the model's output. However, recent work has shown that most existing methods to implement SVAs…
This work studies the dynamic risk management of the risk-neutral value of the potential credit losses on a portfolio of derivatives. Sensitivities-based hedging of such liability is sub-optimal because of bid-ask costs, pricing models…
In this paper, we have studied option pricing methods that are based on a Bayesian Markov-Switching Vector Autoregressive (MS-BVAR) process using a risk-neutral valuation approach. A BVAR process, which is a special case of the Bayesian…
Financial institutions now face the important challenge of having to do multiple portfolio revaluations for their risk computation. The list is almost endless: from XVAs to FRTB, stress testing programs, etc. These computations require from…
This paper studies prediction with multiple candidate models, where the goal is to combine their outputs. This task is especially challenging in heterogeneous settings, where different models may be better suited to different inputs. We…
We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by L\'evy processes, extending earlier works…
In this paper, we develop a theoretical framework for bounding the CVaR of a random variable $X$ using another related random variable $Y$, under assumptions on their cumulative and density functions. Our results yield practical tools for…