Related papers: Pricing Lookback Options on a Quantum Computer
There is increasing interest in quantum algorithms that are based on the imaginary-time evolution (ITE), a successful classical numerical approach to obtain ground states. However, most of the proposals so far require heavy post-processing…
In this paper, we introduce an efficient and end-to-end quantum algorithm tailored for computing the Value-at-Risk (VaR) and conditional Value-at-Risk (CVar) for a portfolio of European options. Our focus is on leveraging quantum…
This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geo-metric Brownian motion; that is, the appreciation rate and the…
We introduce a variational quantum algorithm to solve unconstrained black box binary optimization problems, i.e., problems in which the objective function is given as black box. This is in contrast to the typical setting of quantum…
We present a novel variational quantum framework for linear partial differential equation (PDE) constrained optimization problems. Such problems arise in many scientific and engineering domains. For instance, in aerodynamics, the PDE…
The imaginary-time evolution of quantum states is integral to various fields, ranging from natural sciences to classical optimization or machine learning. Since simulating quantum imaginary-time evolution generally requires storing an…
Double-bracket quantum imaginary-time evolution (DB-QITE) is a quantum algorithm which coherently implements steps in the Riemannian steepest-descent direction for the energy cost function. DB-QITE is derived from Brockett's double-bracket…
Quantum optimization algorithms offer a promising route to finding the ground states of target Hamiltonians on near-term quantum devices. None the less, it remains necessary to limit the evolution time and circuit depth as much as possible,…
This paper concerns the numerical valuation of swing options with discrete action times under a linear two-factor mean-reverting model with jumps. The resulting sequence of two-dimensional partial integro-differential equations (PIDEs) are…
In the regime switching extension of Black-Scholes-Merton model of asset price dynamics, one assumes that the volatility coefficient evolves as a hidden pure jump process. Under the assumption of Markov regime switching, we have considered…
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and…
In this work we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground and excited state estimation on near-term hardware. We derive the theoretical ground on which the…
In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an…
Quantum computers have been proposed as a solution for efficiently solving non-linear differential equations (DEs), a fundamental task across diverse technological and scientific domains. However, a crucial milestone in this regard is to…
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 this paper, we obtain the existence, uniqueness and positivity of the solution to delayed stochastic differential equations with jumps. This equation is then applied to model the price movement of the risky asset in a financial market…
We present a comprehensive quantum algorithm tailored for pricing autocallable options, offering a full implementation and experimental validation. Our experiments include simulations conducted on high-performance computing (HPC) hardware,…
We consider the pricing of derivatives written on accumulated marks, such as weather derivatives or aggregate loss claims, using a self-exciting marked point process. The jump intensity mean-reverts between events and increases at jump…
It is well known that the Black-Scholes-Merton model suffers from several deficiencies. Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in this classical model. Unfortunately, the…
The limitations of the classical Black-Scholes model are examined by comparing calculated and actual historical prices of European call options on stocks from several sectors of the S&P 500. Persistent differences between the two prices…