Related papers: Nonparametric estimates of pricing functionals
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…
In the previous paper (Inverse Problems, 32, 015010, 2016), a new heuristic mathematical model was proposed for accurate forecasting of prices of stock options for 1-2 trading days ahead of the present one. This new technique uses the…
We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finite dimensional Gaussian process (GP)…
This article is a sequel to [A.H.M.P]. In [A.H.M.P], we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic delay equation with fixed delays in the drift and diffusion…
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…
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 implied volatility is a crucial element of any financial toolbox, since it is used for quoting and the hedging of options as well as for model calibration. In contrast to the Black-Scholes formula its inverse, the implied volatility, is…
Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter $q$. A generalized form of the Black-Scholes (B-S) partial differential…
Options have provided a field of much study because of the complexity involved in pricing them. The Black-Scholes equations were developed to price options but they are only valid for European styled options. There is added complexity when…
A version of indifference valuation of a European call option is proposed that includes statistical regularities of nonstochastic randomness. Classical relations (forward contract value and Black-Scholes formula) are obtained as particular…
Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance. The dynamics describing the price of vanilla options when constant volatilities and interest…
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that…
The paper focuses on pricing European-style options on several underlying assets under the Black-Scholes model represented by a nonstationary partial differential equation. The proposed method combines the Galerkin method with…
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the…
This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and…
We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the…
We derive the implied volatility estimation formula in European power call options pricing, where the payoff functions are in the form of $V=(S^{\alpha}_T-K)^{+}$ and $V=(S^{\alpha}_T-K^{\alpha})^{+}$ ($\alpha>0$)respectively. Using…
In this paper, we present a reduced basis method for pricing European and American options based on the Black-Scholes and Heston model. To tackle each model numerically, we formulate the problem in terms of a time dependent variational…
We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous…
We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The…