Related papers: Option pricing and hedging with minimum local expe…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
The variance gamma model is a widely popular model for option pricing in both academia and industry. In this paper, we provide a new perspective for pricing European style options for the variance gamma model by deriving closed-form…
Recent studies have demonstrated the efficiency of Variational Autoencoders (VAE) to compress high-dimensional implied volatility surfaces into a low dimensional representation. Although this method can be effectively used for pricing…
This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential…
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 paper we investigate a nonlinear generalization of the Black-Scholes equation for pricing American style call options in which the volatility term may depend on the underlying asset price and the Gamma of the option. We propose a…
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…
In incomplete financial markets, pricing and hedging European options lack a unique no-arbitrage solution due to unhedgeable risks. This paper introduces a constrained deep learning approach to determine option prices and hedging strategies…
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 analyzes a problem of optimal static hedging using derivatives in incomplete markets. The investor is assumed to have a risk exposure to two underlying assets. The hedging instruments are vanilla options written on a single…
Optimal B-robust estimate is constructed for multidimensional parameter in drift coefficient of diffusion type process with small noise. Optimal mean-variance robust (optimal V -robust) trading strategy is find to hedge in mean-variance…
We consider the mean-variance hedging problem under partial information in the case where the flow of observable events does not contain the full information on the underlying asset price process. We introduce a martingale equation of a new…
Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general,…
The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the…
We introduce a new model of financial market with stochastic volatility driven by an arbitrary H\"older continuous Gaussian Volterra process. The distinguishing feature of the model is the form of the volatility equation which ensures the…
It is shown how to obtain accurate values for American options using Monte Carlo simulation. The main feature of the novel algorithm consists of tracking the boundary between exercise and hold regions via optimization of a certain payoff…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic…
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…
In commodity and energy markets swing options allow the buyer to hedge against futures price fluctuations and to select its preferred delivery strategy within daily or periodic constraints, possibly fixed by observing quoted futures…
The pricing and hedging of a general class of options (including American, Bermudan and European options) on multiple assets are studied in the context of currency markets where trading is subject to proportional transaction costs, and…