Related papers: Pricing Derivatives by Path Integral and Neural Ne…
The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic…
We propose the deep parametric PDE method to solve high-dimensional parametric partial differential equations. A single neural network approximates the solution of a whole family of PDEs after being trained without the need of sample…
Recent advancements in the fields of artificial intelligence and machine learning methods resulted in a significant increase of their popularity in the literature, including electricity price forecasting. Said methods cover a very broad…
In this work we consider one-dimensional generalized affine processes under the paradigm of Knightian uncertainty (so-called non-linear generalized affine models). This extends and generalizes previous results in Fadina et al. (2019) and…
We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…
We develop two alternate approaches to arbitrage-free, market-complete, option pricing. The first approach requires no riskless asset. We develop the general framework for this approach and illustrate it with two specific examples. The…
In this work, we propose an algorithm to price American options by directly solving the dual minimization problem introduced by Rogers. Our approach relies on approximating the set of uniformly square integrable martingales by a finite…
This paper contributes to the literature on parametric demand estimation by using deep learning to model consumer preferences. Traditional econometric methods often struggle with limited within-product price variation, a challenge addressed…
We apply supervised deep neural networks (DNNs) for pricing and calibration of both vanilla and exotic options under both diffusion and pure jump processes with and without stochastic volatility. We train our neural network models under…
A data-driven approach called CaNN (Calibration Neural Network) is proposed to calibrate financial asset price models using an Artificial Neural Network (ANN). Determining optimal values of the model parameters is formulated as training…
Techniques from deep learning play a more and more important role for the important task of calibration of financial models. The pioneering paper by Hernandez [Risk, 2017] was a catalyst for resurfacing interest in research in this area. In…
To pricing health insurance plan, statisticians use mathematical models to predict customers' future health condition. General Addictive Model (GAM) is a wide accepted method for this problem. However, it have several limitations. To solve…
Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of L\'{e}vy driven models of stock markets. In our opinion, any market model should be based on a…
In this article, we analyze two modeling approaches for the pricing of derivative contracts on a commodity index. The first one is a microscopic approach, where the components of the index are modeled individually, and the index price is…
Abstract In this work, we build two environments, namely the modified QLBS and RLOP models, from a mathematics perspective which enables RL methods in option pricing through replicating by portfolio. We implement the environment…
In this paper we study dynamic pricing mechanisms of financial derivatives. A typical model of such pricing mechanism is the so-called g--expectation defined by solutions of a backward stochastic differential equation with g as its…
We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied…
A method for pricing and superhedging European options under proportional transaction costs based on linear vector optimisation and geometric duality developed by Lohne & Rudloff (2014) is compared to a special case of the algorithms for…
Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…