Related papers: Tighter 'uniform bounds for Black-Scholes implied …

Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, {\bf 2}, 415-431, 2002) to include…

The present article provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models as well as American barrier-type options under the Black & Scholes framework. Our method generalizes…

We study the problem of reconstruction of special special time dependent local volatility from market prices of options with different strikes at two expiration times. For a general diffusion process we apply the linearization technique and…

We investigate the relation between the fair price for European-style vanilla options and the distribution of short-term returns on the underlying asset ignoring transaction and other costs. We compute the risk-neutral probability density…

We present ThiopheneIV, a Black-Scholes implied-volatility solver with a monotone core and explicit production guards. The solver starts from the simple Choi-Huh-Su L3 lower-bound seed and applies three Euler-Chebyshev steps on a lower…

Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie…

The space of call price functions has a natural noncommutative semigroup structure with an involution. A basic example is the Black--Scholes call price surface, from which an interesting inequality for Black--Scholes implied volatility is…

We propose a numerical procedure for computing the prices of European options, in which the underlying asset price is a Markovian strict local martingale. If the underlying process is a strict local martingale and the payoff is of linear…

Superlinear convergence has been an elusive goal for black-box nonsmooth optimization. Even in the convex case, the subgradient method is very slow, and while some cutting plane algorithms, including traditional bundle methods, are popular…

This paper deals with an extension of the so-called Black-Scholes model in which the volatility is modeled by a linear combination of the components of the solution of a differential equation driven by a fractional Brownian motion of Hurst…

This article proposes a calibration framework for complex option pricing models that jointly fits market option prices and the term structure of variance. Calibrated models under the conventional objective function, the sum of squared…

The studied model was suggested to design a perfect hedging strategy for a large trader. In this case the implementation of a hedging strategy affects the price of the underlying security. The feedback-effect leads to a nonlinear version of…

Deep learning methods have become a widespread toolbox for pricing and calibration of financial models. While they often provide new directions and research results, their `black box' nature also results in a lack of interpretability. We…

This article studies a Newton-like method already used by several authors but which has not been thouroughly studied yet. We call it the robust-variance scoring (RVS) algorithm because the main version of the algorithm that we consider…

We consider the supervised learning problem of learning the price of an option or the implied volatility given appropriate input data (model parameters) and corresponding output data (option prices or implied volatilities). The majority of…

Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such…

We derive quantitative error bounds for deep neural networks (DNNs) approximating option prices on a $d$-dimensional risky asset as functions of the underlying model parameters, payoff parameters and initial conditions. We cover a general…

A bubble is characterized by the presence of an underlying asset whose discounted price process is a strict local martingale under the pricing measure. In such markets, many standard results from option pricing theory do not hold, and in…

This work focuses on the dynamic hedging of financial derivatives, where a reinforcement learning algorithm is designed to minimize the variance of the delta hedging process. In contrast to previous research in this area, we apply…

In this paper we study the convergence of Newton-Raphson method. For this method there exists some convergence results which are practically not very useful and just guarantee the convergence of this method when the first term of this…