European Options

A statistical technique for cleaning option price data ArXiv ID: 2501.11164 “View on arXiv” Authors: Unknown Abstract Recorded option pricing datasets are not always freely available. Additionally, these datasets often contain numerous prices which are either higher or lower than can reasonably be expected. Various reasons for these unexpected observations are possible, including human error in the recording of the details associated with the option in question. In order for the analyses performed on these datasets to be reliable, it is necessary to identify and remove these options from the dataset. In this paper, we list three distinct problems often found in recorded option price datasets alongside means of addressing these. The methods used are justified using sound statistical reasoning and remove option prices violating the standard assumption of no arbitrage. An attractive aspect of the proposed technique is that no option pricing model-based assumptions are used. Although the discussion is restricted to European options, the procedure is easily modified for use with exotic options as well. As a final contribution, the paper contains a link to six option pricing datasets which have already been cleaned using the proposed methods and can be freely used by researchers. ...

European Option Pricing in Regime Switching Framework via Physics-Informed Residual Learning ArXiv ID: 2410.10474 “View on arXiv” Authors: Unknown Abstract In this article, we employ physics-informed residual learning (PIRL) and propose a pricing method for European options under a regime-switching framework, where closed-form solutions are not available. We demonstrate that the proposed approach serves an efficient alternative to competing pricing techniques for regime-switching models in the literature. Specifically, we demonstrate that PIRLs eliminate the need for retraining and become nearly instantaneous once trained, thus, offering an efficient and flexible tool for pricing options across a broad range of specifications and parameters. ...

Boundary conditions at infinity for Black-Scholes equations ArXiv ID: 2401.05549 “View on arXiv” Authors: Unknown Abstract 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 growth, multiple solutions exist for the corresponding Black-Scholes equations. When numerical schemes such as finite difference methods are applied, a boundary condition at infinity must be specified, which determines a solution among the candidates. The minimal solution, which is considered as the derivative price, is obtained by our boundary condition. The stability of our procedure is supported by the fact that our numerical solution satisfies a discrete maximum principle. In addition, its accuracy is demonstrated through numerical experiments in comparison with the methods proposed in the literature. ...