# Quantum option pricing using Wick rotated imaginary time evolution

@article{Radha2021QuantumOP, title={Quantum option pricing using Wick rotated imaginary time evolution}, author={Santosh Kumar Radha}, journal={Research Papers in Economics}, year={2021} }

In this paper we reformulate the problem of pricing options in a quantum setting. Our proposed algorithm involves preparing an initial state, representing the option price, and then evolving it using existing imaginary time simulation algorithms. This way of pricing options boils down to mapping an initial option price to a quantum state and then simulating the time dependence in Wick's imaginary time space. We numerically verify our algorithm for European options using a particular imaginary…

## 9 Citations

Pricing multi-asset derivatives by variational quantum algorithms

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This work proposes a quantum LSM based on quantum access to a stochastic process, on quantum circuits for computing the optimal stopping times, and on quantum techniques for Monte Carlo that achieves a nearly quadratic speedup in the runtime compared to the LSM algorithm.

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The results shed light on the connection between quantum quantile mechanics (QQM) and qGANs for SDE-based distributions, and point the importance of differential constraints for model training, analogously with the recent success of physics informed neural networks.

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A quantum machine learning approach to learn the mixer Hamiltonian that is required to hard constrain the search subspace is introduced and it is shown that this method can be used for encoding any general form of constraints.

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An approach for learning probability distributions as differentiable quantum circuits (DQC) that enable efficient quantum generative modelling (QGM) and synthetic data generation and shows how samples from solutions of stochastic differential equations (SDEs) can be accessed by solving stationary and time-dependent Fokker-Planck equations with a quantum protocol.

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