Related papers: Tighter 'uniform bounds for Black-Scholes implied …
We train neural networks to learn optimal replication strategies for an option when two replicating instruments are available, namely the underlying and a hedging option. If the price of the hedging option matches that of the Black--Scholes…
Options are contingent claims regarding the value of underlying assets. The Black-Scholes formula provides a road map for pricing these options in a risk-neutral setting, justified by a delta hedging argument in which countervailing…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis…
In the present work, we propose a new multifactor stochastic volatility model in which slow factor of volatility is approximated by a parabolic arc. We retain ourselves to the perturbation technique to obtain approximate expression for…
Option prices encode the market's collective outlook through implied density and implied volatility. An explicit link between implied density and implied volatility translates the risk-neutrality of the former into conditions on the latter…
We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied…
This paper proposes a deep delta hedging framework for options, utilizing neural networks to learn the residuals between the hedging function and the implied Black-Scholes delta. This approach leverages the smoother properties of these…
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…
Extracting implied information, like volatility and/or dividend, from observed option prices is a challenging task when dealing with American options, because of the computational costs needed to solve the corresponding mathematical problem…
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the…
Deep hedging is a framework for hedging derivatives in the presence of market frictions. In this study, we focus on the problem of hedging a given target option by using multiple options. To extend the deep hedging framework to this…
In this paper we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. This formula is useful for pricing and risk management as…
We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments…
The Black-Scholes theory of option pricing has been considered for many years as an important but very approximate zeroth-order description of actual market behavior. We generalize the functional form of the diffusion of these systems and…
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…
It is well-known that the Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This paper…
The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility which can be a function of the second derivative of the option price itself. A…
This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being…
We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European,…