Related papers: A perturbative moment approach to option pricing
In this paper, we study option pricing under Vasicek Model by a Hamiltonian approach. Since the interest rate changes with time, we split the time to maturity into infinite steps, and the matrix element during each step could be calculated…
In this paper we study recent developments in the approximation of the spread option pricing. As the Kirk\'s Approximation is extremely flawed in the cases when the correlation is very high, we explore a recent development that allows…
The aim of this study is to devise numerical methods for dealing with very high-dimensional Bermudan-style derivatives. For such problems, we quickly see that we can at best hope for price bounds, and we can only use a simulation approach.…
Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…
In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well-known decomposition of an American option price with that of a European option…
In this paper we present an algorithm for pricing barrier options in one-dimensional Markov models. The approach rests on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given…
Based on the canonical correlation analysis we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as…
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…
Intractable distributions present a common difficulty in inference within the probabilistic knowledge representation framework and variational methods have recently been popular in providing an approximate solution. In this article, we…
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…
This paper aims to provide a practical example on the assessment and propagation of input uncertainty for option pricing when using tree-based methods. Input uncertainty is propagated into output uncertainty, reflecting that option prices…
The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion process. The present paper aims to give a mathematical credit to the…
In this Article, a fast numerical numerical algorithm for pricing discrete double barrier option is presented. According to Black-Scholes model, the price of option in each monitoring date can be evaluated by a recursive formula upon the…
The probability density function (PDF) of some global average quantity plays a fundamental role in critical and highly correlated systems. We explicitly compute this quantity as a function of the magnetization for the two dimensional XY…
In this paper, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic…
We introduce an approximation strategy for the discounted moments of a stochastic process that can, for a large class of problems, approximate the true moments. These moments appear in pricing formulas of financial products such as bonds…
We address the problem of approximating the moments of the solution, $\boldsymbol{X}(t)$, of an It\^o stochastic differential equation (SDE) with drift and a diffusion terms over a time-grid $t_0, t_1, \ldots, t_n$. In particular, we assume…
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…
An American option grants the holder the right to select the time at which to exercise the option, so pricing an American option entails solving an optimal stopping problem. Difficulties in applying standard numerical methods to complex…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…