Related papers: Pricing and hedging barrier options in a hyper-exp…
This paper presents the solution to a European option pricing problem by considering a regime-switching jump diffusion model of the underlying financial asset price dynamics. The regimes are assumed to be the results of an observed pure…
We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we…
We present a differential machine learning method for zero-days-to-expiry (0DTE) options under a stochastic-volatility jump-diffusion model. To handle the ultra-short-maturity regime, we express the option price in Black-Scholes form with a…
We propose a constructive framework for the super-hedging problem of a European contingent claim under proportional transaction costs in discrete time. Our main contribution is an explicit recursive scheme that computes both the…
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…
We provide closed-form pricing formulas for a wide variety of path-independent options, in the exponential L\'evy model driven by the Normal inverse Gaussian process. The results are obtained in both the symmetric and asymmetric model, and…
In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the…
We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…
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…
The approach that allows find European option price on the assumption of hedging at discrete times is proposed. The routine allows find the option price not for lognormal distribution functions of underlying asset only but for wide enough…
This paper presents the Runge-Kutta-Legendre finite difference scheme, allowing for an additional shift in its polynomial representation. A short presentation of the stability region, comparatively to the Runge-Kutta-Chebyshev scheme…
It is well known that the Black-Scholes-Merton model suffers from several deficiencies. Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in this classical model. Unfortunately, the…
We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an…
The author presents alternatives to the Black-Scholes european call option pricing model by incorporating different transaction cost structures in the replicating strategy. In particular, an exponentially decreasing structure is proposed…
In the present paper we present a finite element approach for option pricing in the framework of a well-known stochastic volatility model with jumps, the Bates model. In this model the asset log-returns are assumed to follow a…
We model the price of a stock via a Lang\'{e}vin equation with multi-dimensional fluctuations coupled in the price and in time. We generalize previous models in that we assume that the fluctuations conditioned on the time step are compound…
We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential L\'evy models driven by one-sided stable or tempered stable processes. Pricing formulas take…
In the first quarter of 2006 Chicago Board Options Exchange (CBOE) introduced, as one of the listed products, options on its implied volatility index (VIX). This created the challenge of developing a pricing framework that can…
We show that prices and shortfall risks of game (Israeli) barrier options in a sequence of binomial approximations of the Black--Scholes (BS) market converge to the corresponding quantities for similar game barrier options in the BS market…
A new approximate Bayesian inferential framework is proposed that exploits multiple information sources -- daily spot returns, high-frequency spot data and option prices -- and enables fast calculation of probabilistic predictions of future…