Related papers: Nonparametric estimates of pricing functionals

In this work we present an analytical model, based on the path-integral formalism of Statistical Mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under…

Financial markets based on L\'evy processes are typically incomplete and option prices depend on risk attitudes of individual agents. In this context, the notion of utility indifference price has gained popularity in the academic circles.…

In this paper, a new numerical method based on adaptive gradient descent optimizers is provided for computing the implied volatility from the Black-Scholes (B-S) option pricing model. It is shown that the new method is more accurate than…

We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with…

In this work, we give a generalized formulation of the Black-Scholes model. The novelty resides in considering the Black-Scholes model to be valid on 'average', but such that the pointwise option price dynamics depends on a measure…

This study investigates the application of machine learning techniques, specifically Neural Networks, Random Forests, and CatBoost for option pricing, in comparison to traditional models such as Black-Scholes and Heston Model. Using both…

We propose a financial market model that comprises a savings account and a stock. The stock price process is modeled as a one-dimensional diffusion, in which two types of agents exist: an ordinary investor and a fundraiser who buys or sells…

This paper implements an efficient numerical algorithm for the time-fractional Black-Scholes model governing European options. The proposed method comprises the Crank-Nicolson approach to discretize the time variable and exponential…

Presented is intuitive proof of Black-Scholes formula for European call options, which is based on arbitrage and properties of lognormal distribution. Paper can help students and non-mathematicians to better understand economic concepts…

We solve the superhedging problem for European options in an illiquid extension of the Black-Scholes model, in which transactions have transient price impact and the costs and the strategies for hedging are affected by physical or cash…

Using the option delta systematically, we derive tighter lower and upper bounds of the Black-Scholes implied volatility than those in Tehranchi [SIAM J. Financ. Math. 7 (2016), 893-916]. As an application, we propose a Newton-Raphson…

In financial mathematics, it is a typical approach to approximate financial markets operating in discrete time by continuous-time models such as the Black Scholes model. Fitting this model gives rise to difficulties due to the discrete…

We consider a model of linear market impact, and address the problem of replicating a contingent claim in this framework. We derive a non-linear Black-Scholes Equation that provides an exact replication strategy. This equation is fully…

The accurate valuation of financial derivatives plays a pivotal role in the finance industry. Although closed formulas for pricing are available for certain models and option types, exemplified by the European Call and Put options in the…

We propose a parameter-free model for estimating the price or valuation of financial derivatives like options, forwards and futures using non-supervised learning networks and Monte Carlo. Although some arbitrage-based pricing formula…

A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black--Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option…

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 unified analytical pricing framework with involvement of the shot noise random process has been introduced and elaborated. Two exactly solvable new models have been developed. The first model has been designed to value options. It is…

An option market maker incurs funding costs when carrying and hedging inventory. To hedge a net long delta inventory, for example, she pays a fee to borrow stock from the securities lending market. Because of haircuts, she posts additional…

In this paper, we present an implicit finite difference method for the numerical solution of the Black-Scholes model of American put options without dividend payments. We combine the proposed numerical method by using a front fixing…