Related papers: Some pricing tools for the Variance Gamma model
It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for several probability distributions arising in practice a…
We consider the problem of pricing path-dependent options on a basket of underlying assets using simulations. As an example we develop our studies using Asian options. Asian options are derivative contracts in which the underlying variable…
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…
We prove simple general formulas for expectations of functions of a random walk and its running extremum. Under additional conditions, we derive analytical formulas using the inverse $Z$-transform, the Fourier/Laplace inversion and…
Many methods that build powerful variational distributions based on unadjusted Langevin transitions exist. Most of these were developed using a wide range of different approaches and techniques. Unfortunately, the lack of a unified analysis…
Here we develop an option pricing method based on Legendre series expansion of the density function. The key insight, relying on the close relation of the characteristic function with the series coefficients, allows to recover the density…
Risk assessment and in particular derivatives pricing is one of the core areas in computational finance and accounts for a sizeable fraction of the global computing resources of the financial industry. We outline a quantum-inspired…
We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for…
Based on the Lie symmetry method, we investigate a Feynman-Kac formula for the classical geometric mean reversion process, which effectively describing the dynamics of short-term interest rates. The Lie algebra of infinitesimal symmetries…
In this paper we give easy-to-implement closed-form expressions for European and Asian Greeks for general L2-payoff functions and underlying assets in an exponential L\'evy process model with nonvanishing Brownian motion part. The results…
Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally…
New fast estimation methods stemming from control theory lead to a fresh look at time series, which bears some resemblance to "technical analysis". The results are applied to a typical object of financial engineering, namely the forecast of…
For a converging sequence of exponential L\'evy models, we give conditions under which the associated sequence of option prices converges. We also study the behaviour of the prices when no such convergence holds. We then consider two…
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same…
Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme…
Evaluating financial products with early-termination clauses, in particular those with path-dependent structures, is challenging. This paper focuses on Asian options, look-back options, and callable certificates. We will compare regression…
A fast algorithm for path sampling in path integral Monte Carlo simulations is proposed. The algorithm utilizes the Levy-Ciesielski implementation of Lie-Trotter products to achieve a mathematically proven computational cost of n*log_2(n)…
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to…
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…
We study prior-independent pricing for selling a single item to a single buyer when the seller observes only a single sample from the valuation distribution, while the buyer knows the distribution. Classical robust pricing approaches either…