相关论文: Fast computation of vanilla prices in time-changed…

In this paper we use Bernstein and Chebyshev polynomials to approximate the price of some basket options under a bivariate Black-Scholes model. The method consists in expanding the price of a univariate related contract after conditioning…

Volatility modelling has become a significant area of research within Financial Mathematics. Wiener process driven stochastic volatility models have become popular due their consistency with theoretical arguments and empirical observations.…

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…

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error…

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…

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…

The article is devoted to models of financial markets with stochastic volatility, which is defined by a functional of Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question of exact price of European option. The…

Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an…

We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is…

The accurate valuation of financial derivatives plays a pivotal role in the finance industry. Although closed formulas for pricing are available for certain models and option types, exemplified by the European Call and Put options in the…

In this paper a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with…

G-expectation, as a sublinear expectation, provides a powerful framework for modeling uncertainty in financial markets. Motivated by the need for robust valuation under model uncertainty, this work develops a unified risk-neutral valuation…

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…

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…

Since the introduction of the Black-Scholes model stochastic processes have played an increasingly important role in mathematical finance. In many cases prices, volatility and other quantities can be modeled using stochastic ordinary…

In a seminal paper in 1973, Black and Scholes argued how expected distributions of stock prices can be used to price options. Their model assumed a directed random motion for the returns and consequently a lognormal distribution of asset…

We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of…

Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range…

In this paper we propose an efficient method to compute the price of multi-asset American options, based on Machine Learning, Monte Carlo simulations and variance reduction technique. Specifically, the options we consider are written on a…

Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented…