Finance

The Classiq financial package provides a rich interface to automatically generate and execute quantum programs for various financial problems such as options pricing and risk analysis.

Background

Complex models and simulations, borrowed from the world of physics, are very common in finance. Many of these models are stochastic. Hence, numerical methods have to be employed to solve them. The most popular model is Monte Carlo [1] due to its flexibility and ability to handle stochastic parameters generically. Classical Monte Carlo methods, however, generally require extensive computational resources to provide an accurate estimation. By leveraging the laws of quantum mechanics, a quantum computer may provide novel ways to solve such computationally intensive financial problems. Relevant financial applications include risk management and option pricing. The core of several of these applications is the amplitude estimation algorithm [2] , which can estimate a parameter with a convergence rate of 1/M, where M is the number of Grover iterations, representing a theoretical quadratic speed-up over classical Monte Carlo methods.

Other financial models such as portfolio optimizations can be modeled by the Classiq combinatorial optimization methods.

References

[1] Paul Glasserman, Monte Carlo Methods in Financial Engineering. Springer-Verlag New York, 2003, p. 596.

[2] Gilles Brassard, Peter Hoyer, Michele Mosca, and Alain Tapp, Quantum Amplitude Amplification and Estimation, Contemporary Mathematics 305 (2002).