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We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift,…
In this paper, we aim to compute numerical approximation integral by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called…
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different…
When gradient-based methods are impractical, black-box optimization (BBO) provides a valuable alternative. However, BBO often struggles with high-dimensional problems and limited trial budgets. In this work, we propose a novel approach…
This paper explores the application of Machine Learning techniques for pricing high-dimensional options within the framework of the Uncertain Volatility Model (UVM). The UVM is a robust framework that accounts for the inherent…
This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being…
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is…
We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, termed variational boosting, iteratively refines an existing variational approximation…
Financial derivative pricing is a significant challenge in finance, involving the valuation of instruments like options based on underlying assets. While some cases have simple solutions, many require complex classical computational methods…
Black-Scholes (BS) is the standard mathematical model for option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS…
We consider the problem of approximation of density functions which is important in the theory of pricing of basket options. Our method is well adopted to the multidimensional case. Observe that implementations of polynomial and spline…
In mathematical finance, a process of calibrating stochastic volatility (SV) option pricing models to real market data involves a numerical calculation of integrals that depend on several model parameters. This optimization task consists of…
We compare static arbitrage price bounds on basket calls, i.e. bounds that only involve buy-and-hold trading strategies, with the price range obtained within a multi-variate generalization of the Black-Scholes model. While there is no gap…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
Neural networks with sufficiently smooth activation functions can approximate values and derivatives of any smooth function, and they are differentiable themselves. We improve the approximation capability of neural networks by utilizing the…
We investigate the use of Malliavin calculus in order to calculate the Greeks of multidimensional complex path-dependent options by simulation. For this purpose, we extend the formulas employed by Montero and Kohatsu-Higa to the…
We study the principal component analysis based approach introduced by Reisinger & Wittum (2007) and the comonotonic approach considered by Hanbali & Linders (2019) for the approximation of American basket option values via multidimensional…
In this paper, we study a retailer price optimization problem which includes the practical constraints: maximum number of price changes and minimum amount of price change (if a change is recommended). We provide a closed-form formula for…
We analyze the empirical performance of several non-parametric estimators of the pricing functional for European options, using historical put and call prices on the S&P500 during the year 2012. Two main families of estimators are…
We present a new high-order compact scheme for the multi-dimensional Black-Scholes model with application to European Put options on a basket of two underlying assets. The scheme is second-order accurate in time and fourth-order accurate in…