D5.7 Update of review of state-of-the-art for Pricing and Computation of VaR

Derivatives contracts are one of the fundamental pillars of modern financial markets and are routinely traded by both financial institutions and traders with a variety of objectives, such as financial risk hedging. For this reason, the fair valuation of financial derivatives, known as pricing, and the computation of various risk measures, such as the Value at Risk (VaR), have become two of the tasks that consume a great amount of computational resources in financial institutions. Classically, the problems of derivatives pricing and the computation of VaR are mainly solved by means of Monte Carlo-simulation (MC) techniques or numerical algorithms for solving partial differential equations (PDE). The key advantage of MC technique is that it is easy to implement, very general and scales well with the dimension of the problem. Therefore, it has become the de facto standard by financial institutions to tackle both problems. In this context, NExt ApplicationS of Quantum Computing (NEASQC) Use Case 5 (UC5) works on the de-velopment and evaluation of quantum algorithms for derivatives pricing and VaR problems. Inspired by the aforementioned classical algorithms, the quantum computing community has developed different strategies to speed up the classical techniques. This report summarises the advances on derivatives pricing and the computation of VaR since the publication of the deliverable D5.3 review. The report is divided in three main sections. The first section corresponds to the main line of research on quantum computing for pricing and VaR, namely, Quantum Accelerated Monte Carlo (QAMC). This technique promises to be as flexible and general as its classical counterpart while requiring quadratically fewer computational steps. The second section corresponds to quantum algorithms for solving Partial Differential Equations (PDEs). In this case it is possible to find some methods that promise to obtain even exponential speedups. However, such speedups can only be attained for very specific cases which makes it less attractive for practitioners. The last section is devoted to different techniques which do not fall in the previous two categories. Thus, we include recent advances on quantum machine learning techniques applied to finance, financial modeling via quantum mechanics and quantum assets. It is important to note that some of the proposed techniques require far more quantum computational resources than are currently available. This includes limitations in the number of qubits, in the depth of the circuits and in the levels of “noise”. Hence, the current deliverable pays special focus to quantum algorithms in Noisy Intermediate-Scale Quantum (NISQ) computers