Related papers: A Path Integral Approach to Derivative Security Pr…
The goal of this paper is to define stochastic integrals and to solve stochastic differential equations for typical paths taking values in a possibly infinite dimensional separable Hilbert space without imposing any probabilistic structure.…
We introduce signature payoffs, a family of path-dependent derivatives that are given in terms of the signature of the price path of the underlying asset. We show that these derivatives are dense in the space of continuous payoffs, a result…
In this paper we develop numerical pricing methodologies for European style Exchange Options written on a pair of correlated assets, in a market with finite liquidity. In contrast to the standard multi-asset Black-Scholes framework, trading…
Path integral Monte Carlo with Green's function analysis allows the sampling of quantum mechanical properties of molecules at finite temperature. While a high-precision computation of the energy of the Born-Oppenheimer surface from path…
In this paper we study partial differential equations (PDEs) that can be used to model value adjustments. Different value adjustments denoted generally as xVA are nowadays added to the risk-free financial derivative values and the PDE…
Importance sampling is a promising variance reduction technique for Monte Carlo simulation based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm…
This paper explores advancements in quantum algorithms for derivative pricing of exotics, a computational pipeline of fundamental importance in quantitative finance. For such cases, the classical Monte Carlo integration procedure provides…
A simple and efficient method for quantum Monte Carlo simulation is presented, based on discretization of the action in the path integral, and a Gaussian averaging of the potential, which works well e.g. with the Coulomb potential.
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…
In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a given time maturity of some stochastic volatility model with unbounded drift. Relying on a perturbation…
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…
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…
Optimal pricing of European call option is described by linear stochastic differential equation. Trading strategy given by a twin of stochastic variables was integrated w.r.t. Black-Scholes formula to adopt optimal pricing to tarading…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: Stochastic approximation replaces regression in the LSM algorithm; Explicit…
This paper introduces a no-arbitrage, Monte Carlo-free approach to pricing path-dependent interest rate derivatives. The Heath-Jarrow-Morton model gives arbitrage-free contingent claims prices but is infinite-dimensional, making traditional…
In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite…
For the numerical solution of Dirichlet-type boundary value problems associated to nonlinear fractional differential equations of order $\alpha \in (1,2)$ that use Caputo derivatives, we suggest to employ shooting methods. In particular, we…
The use of sequential Monte Carlo within simulation for path-dependent option pricing is proposed and evaluated. Recently, it was shown that explicit solutions and importance sampling are valuable for efficient simulation of spot price and…
We consider option pricing using a discrete-time Markov switching stochastic volatility with co-jump model, which can model volatility clustering and varying mean-reversion speeds of volatility. For pricing European options, we develop a…