Quantum computational finance: Monte Carlo pricing of financial derivatives

Abstract

This work presents a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant probability distributions can be prepared in quantum superposition, the payoff functions can be implemented via quantum circuits, and the price of financial derivatives can be extracted via quantum measurements. We show how the amplitude estimation algorithm can be applied to achieve a quadratic quantum speedup in the number of steps required to obtain an estimate for the price with high confidence. This work provides a starting point for further research at the interface of quantum computing and finance.

Quantum computing for finance: Overview and prospects

“…Building upon Montanaro's work, Rebentrost, Gupt, and Bromley suggested using quantum-accelerated Monte Carlo to obtain a quadratic speedup in pricing financial derivatives [11]. The idea is to design a quantum operator which has the same probability distribution as the financial derivative, and apply the method from Ref.…”

“…[10] to estimate its expectation value. Rebentrost et al also discuss how their method can be applied to the pricing of a European call option and to Asian options [11].…”

“…The act of sampling a distribution function can limit the speed, and hence the applicability, of the algorithm. In a series of recent papers, it was suggested this task could be done efficiently by sampling a quantum system [9][10][11].…”

Overview and Comparison of Gate Level Quantum Software Platforms

“…The language contains both classical and quantum control flow, "pseudo-classical" operators, and abilities to implement query transformations required for "black box" algorithms like the standard Deutsch-Jozsa and Bernstein-Vazirani algorithms. Short example programs to get an idea for the QCL syntax, as well as 12 See https://qutech.nl/qx-quantum-computer-simulator/. longer programs implementing algorithms like Grover and Shor, can be found in [8].…”

“…These computers are small, noisy, and not nearly as powerful as current classical computers. But they are nascent, steadily growing, and heralding a future of vast computational power for problems in chemistry [7,8], machine learning [9,10], optimization [11], finance [12], and more [13]. These devices are a testbed for preparing the next generation of quantum software engineers to tackle current classically intractable computational problems.…”