Related papers: Path Integral Method for Pricing Proportional Step…
We propose a very efficient method for pricing various types of lookback options under Markov models. We utilize the model-free representations of lookback option prices as integrals of first passage probabilities. We combine efficient…
After a brief review of the derivation of the standard phase time formula, based on the use of the stationary phase method, we propose, in the opaque limit, an alternative method to calculate the phase time. The new formula for the phase…
The Feynman path integral approach to quantum mechanics is examined in the case where the configuration space is curved. It is shown how the ambiguity that is present in the choice of path integral measure may be resolved if, in addition to…
This paper introduces a semi-analytical method for pricing American options on assets (stocks, ETFs) that pay discrete and/or continuous dividends. The problem is notoriously complex because discrete dividends create abrupt price drops and…
For pricing American options, %after suitable discretization in space and time, a sequence of discrete linear complementarity problems (LCPs) or equivalently Hamilton-Jacobi-Bellman (HJB) equations need to be solved in a sequential…
We reconsider the valuation of barrier options by means of binomial trees from a "forward looking" prospective rather than the more conventional "backward induction" one used by standard approaches. This reformulation allows us to write…
The exchange antisymmetry between identical fermions gives rise to the well known fermion sign problem, in the form of large cancellation between positive and negative contribution to the partition function, making any simulation methods…
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
After a market downturn, especially in an uncertain economic environment such as the current state, there can be a relatively long period with a sideways market, where indexes, stocks, etc., move in channels with support and resistance…
This paper presents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a type of generalised stochastic hybrid system that integrates continuous dynamics with discrete jump processes. Standard…
We give a pedagogical review of the application of field theoretic and path integral methods to calculate moments of the probability density function of stochastic differential equations perturbatively.
We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model. Our approach is based on the equivalence between the pricing partial differential equation…
Barrier options are one of the most widely traded exotic options on stock exchanges. In this paper, we develop a new stochastic simulation method for pricing barrier options and estimating the corresponding execution probabilities. We show…
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
Within a path integral formalism for non-Gaussian price fluctuations we set up a simple stochastic calculus and derive a natural martingale for option pricing from the wealth balance of options, stocks, and bonds. The resulting formula is…
The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete…
In this paper we propose a semi-analytic approach to pricing American options for time-dependent jump-diffusions models with exponential jumps The idea of the method is to further generalize our approach developed for pricing barrier,…
The fractional quantum and statistical mechanics have been developed via new path integrals approach.
Financial derivative pricing is a significant challenge in finance, involving the valuation of instruments like options based on underlying assets. While some cases have simple solutions, many require complex classical computational methods…