Related papers: Nonparametric estimates of pricing functionals
We investigate whether it is possible to formulate option pricing and hedging models without using probability. We present a model that is consistent with two notions of volatility: a historical volatility consistent with statistical…
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…
The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets…
This paper performs the numerical analysis and the computation of a Spread option in a market with imperfect liquidity. The number of shares traded in the stock market has a direct impact on the stock's price. Thus, we consider a…
We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Al\`os in [2] for the Heston model. We realize that a new term arises when the stock…
We present a novel method for the numerical pricing of American options based on Monte Carlo simulation and the optimization of exercise strategies. Previous solutions to this problem either explicitly or implicitly determine so-called…
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…
Options financial instruments designed to protect investors from the stock market randomness. In 1973, Fisher Black, Myron Scholes and Robert Merton proposed a very popular option pricing method using stochastic differential equations…
No--arbitrage property provides a simple method for pricing financial derivatives. However, arbitrage opportunities exist among different markets in various fields, even for a very short time. By knowing that an arbitrage property exists,…
We present a fully nonparametric method to estimate the value function, via simulation, in the context of expected infinite-horizon discounted rewards for Markov chains. Estimating such value functions plays an important role in approximate…
We present a method for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, which is based on a system of integral equations that relates terminal density and option prices. Using a discretization of…
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…
Barrieu, Rouault, and Yor [J. Appl. Probab. 41 (2004)] determined asymptotics for the logarithm of the distribution function of the Hartman-Watson distribution. We determine the asymptotics of the density. This refinement can be applied to…
We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic…
This paper explores the use of deep residual networks for pricing European options on Petrobras, one of the world's largest oil and gas producers, and compares its performance with the Black-Scholes (BS) model. Using eight years of…
The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes…
The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent…
We describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of…
We deal with some generalizations on a Black--Scholes model arising in financial mathematics. As novelty in this paper, we consider a variable volatility and abstract functional boundary conditions, which allow us to treat a very large…
The present article provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models as well as American barrier-type options under the Black & Scholes framework. Our method generalizes…