Related papers: L\'{e}vy driven models and derivative pricing
We review an algorithm developed for parameter estimation within the Continuous Data Assimilation (CDA) approach. We present an alternative derivation for the algorithm presented in a paper by Carlson, Hudson, and Larios (CHL, 2021). This…
The presence of discrete dividends complicates the derivation and form of pricing formulas even for vanilla options. Existing analytic, numerical, and theoretical approximations provide results of varying quality and performance. Here, we…
This paper discusses the connection between mathematical finance and statistical modelling which turns out to be more than a formal mathematical correspondence. We like to figure out how common results and notions in statistics and their…
L\'{e}vy processes with completely monotone jumps appear frequently in various applications of probability. For example, all popular stock price models based on L\'{e}vy processes (such as the Variance Gamma, CGMY/KoBoL and Normal Inverse…
We introduce a simple framework in which market participants update their prior about an efficient price with a model-based learning process. We show that exponential intensities for the arrival of aggressive orders arise naturally in this…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
A rich supply of data and innovative algorithms have made data-driven modeling a popular technique in modern industry. Among various data-driven methods, latent variable models (LVMs) and their counterparts account for a major share and…
In this paper we study the pricing of exchange options under a dynamic described by stochastic correlation with random jumps. In particular, we consider a Ornstein-Uhlenbeck covariance model with Levy Background Noise Process driven by…
We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is…
Several versions of It\^{o}'s formula have been obtained in the context of the functional stochastic calculus. Here, we revisit this topic in two ways. First, by defining a notion of derivative along a functional, we extend the setting of…
In a market with transaction costs, the price of a derivative can be expressed in terms of (preconsistent) price systems (after Kusuoka (1995)). In this paper, we consider a market with binomial model for stock price and discuss how to…
Data play an increasingly important role in smart data analytics, which facilitate many data-driven applications. The goal of various data markets aims to alleviate the issue of isolated data islands, so as to benefit data circulation. The…
Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep…
The literature on volatility modelling and option pricing is a large and diverse area due to its importance and applications. This paper provides a review of the most significant volatility models and option pricing methods, beginning with…
The Shapley value has been proposed as a solution to many applications in machine learning, including for equitable valuation of data. Shapley values are computationally expensive and involve the entire dataset. The query for a point's…
Motivated by a recent surge of interest for Dynkin operators in mathematical physics and by problems in the combinatorial theory of dynamical systems, we propose here a systematic study of logarithmic derivatives in various contexts. In…
The additive process generalizes the L\'evy process by relaxing its assumption of time-homogeneous increments and hence covers a larger family of stochastic processes. Recent research in option pricing shows that modeling the underlying log…
In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the…
This paper considers the modelling of collateralized debt obligations (CDOs). We propose a top-down model via forward rates generalizing Filipovi\'c, Overbeck and Schmidt (2009) to the case where the forward rates are driven by a finite…
We propose a parsimonious stochastic model for characterising the distributional and temporal properties of rainfall. The model is based on an integrated Ornstein-Uhlenbeck process driven by the Hougaard L\'evy process. We derive properties…