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Collateralized debt obligation (CDO) has been one of the most commonly used structured financial products and is intensively studied in quantitative finance. By setting the asset pool into different tranches, it effectively works out and…
Recent studies have demonstrated the efficiency of Variational Autoencoders (VAE) to compress high-dimensional implied volatility surfaces into a low dimensional representation. Although this method can be effectively used for pricing…
It is known from previous work of the authors that non-negative arbitrage free price processes in finance can be described in terms of filtered likelihood processes of statistical experiments and vice versa. The present paper summarizes and…
A critical problem in the financial world deals with the management of risk, from regulatory risk to portfolio risk. Many such problems involve the analysis of securities modelled by complex dynamics that cannot be captured analytically,…
The pricing of currency options is largely dependent on the dynamic relationship between a pair of currencies. Typically, the pricing of options with payoffs dependent on multi-assets becomes tricky for reasons such as the non-Gaussian…
In this paper, we introduce two novel methods to solve the American-style option pricing problem and its dual form at the same time using neural networks. Without applying nested Monte Carlo, the first method uses a series of neural…
The problem of European-style option pricing in time-changed L\'{e}vy models in the presence of compound Poisson jumps is considered. These jumps relate to sudden large drops in stock prices induced by political or economical hits. As the…
In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite…
In this paper we present two parallel Monte Carlo based algorithms for pricing multi--dimensional Bermudan/American options. First approach relies on computation of the optimal exercise boundary while the second relies on classification of…
In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
In this paper, we price European Call three different option pricing models, where the volatility is dynamically changing i.e. non constant. In stochastic volatility (SV) models for option pricing a closed form approximation technique is…
We propose a new framework to value employee stock options (ESOs) that captures multiple exercises of different quantities over time. We also model the ESO holder's job termination risk and incorporate its impact on the payoffs of both…
We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a…
We discuss the Bayesian emulation approach to computational solution of multi-step portfolio studies in financial time series. "Bayesian emulation for decisions" involves mapping the technical structure of a decision analysis problem to…
In this work, we adapt a Monte Carlo algorithm introduced by Broadie and Glasserman (1997) to price a $\pi$-option. This method is based on the simulated price tree that comes from discretization and replication of possible trajectories of…
We introduce a stacking version of the Monte Carlo algorithm in the context of option pricing. Introduced recently for aeronautic computations, this simple technique, in the spirit of current machine learning ideas, learns control variates…
The use of sequential Monte Carlo within simulation for path-dependent option pricing is proposed and evaluated. Recently, it was shown that explicit solutions and importance sampling are valuable for efficient simulation of spot price and…
The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion process. The present paper aims to give a mathematical credit to the…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic…