Mizuho–DL Financial Technology Co., Ltd.Mizuho–DL Financial Technology Co., Ltd.


Research and Studies

Quantum Pricing with a Smile: Implementation of Local Volatility Model on Quantum Computer

Date:Jul. 3, 2020
Author:Kazuya Kaneko/Koichi Miyamoto/Naoyuki Takeda/Kazuyoshi Yoshino

It is expected that quantum computers speed up Monte Carlo simulations. Especially, its application to derivative pricing has been investigated. However, most of existing studies focused only on the Black-Scholes model, which is canonical but simple. Therefore, it is necessary to extend the research targets to advanced models, for which Monte Carlo simulation is used in practice. In our paper, we focus on the local volatility (LV) model, which is widely used in practice, and consider how to implement it on quantum computers. Based on the pseudorandom-number-based scheme, which we previously proposed (Miyamoto and Shiohara, Phys. Rev. A102, 022424), we present the concrete and detailed quantum circuits for time evolution of underlying asset prices in the LV model, and estimate the required resources, qubit number and gate number.

A novel method for reduction of qubits in Monte Carlo simulation by quantum computers

Date:Nov. 28, 2019
Author:Koichi Miyamoto/Kenji Shiohara(Intern)

Following the recent rapid advance of quantum computing, many researchers are investigating its application to finance.
One important example is the quantum speedup of Monte Carlo simulation, which is used, for example, for risk measurement in financial institutions.
Here, the number of qubits, units of quantum computation, can be problematic.
That is, in many problems in finance it is necessary to generate many random numbers in simulations, and therefore a huge number of qubit are required in order to express many random numbers in the implementation in previous papers.
In our paper, we propose a method to reduce qubits, based on a numerical method used in the current practice in financial firms.
In this method, we implement a pseudo-random number generator on a quantum computer and sequentially generate pseudo-random numbers.
This makes the number of required qubits independent from the number of random numbers.

Patents both in Japan and in the US granted for a random number generation on a GPU

Date:Sep. 1, 2014
Author:Tomohisa Yamakami

We are pleased to announce that we have earned patents for a method and apparatus of random number generation by a GPU in Japan and in the US.
The invention is for a method to parallelize to generate random numbers without changing its sequence, when we convert existing codes for GPU computing to speed up.
It is possible to minimize the numerical differences between CPU and GPU.
This has the effect of reducing the work relating to the development and verification of GPU computing and we will be able to respond to customer needs quickly.
(Japan patent number 5059928 and US patent number 8786617.)

A comprehensive framework for implementing quantitative stress tests

Date:Dec. 27, 2013

In this paper, we propose an extension of the firm–value model, which is a standard method for measuring credit risk, so that the model can incorporate the information about macroeconomic indicators. We also explain the method for performing macro stress tests with this model. The extension, which is consistent with the firm–value model, has several advantages. First, we can perform a wide range of analyses with a lot of macroeconomic indicators taken into account. Second, we can calculate credit risk measures under stressed conditions at industry– or firm–level. Finally, stress tests are easy to implement with this model, thereby enabling us to examine various stress scenarios. Using this method, we can identify the weak points of a credit portfolio and obtain the information useful for working out effective action plans. In addition, we propose a method for performing reverse stress tests with the extended firm–value model.

Patents both in Japan and in the US granted for a fast and highly accurate method of calculating credit risks of portfolios

Date:Apr. 23, 2010

We are pleased to announce that we have granted patents both in Japan and in the United States for a method and apparatus of quickly and accurately calculating credit risks of portfolios.
Please see the document here for more information about this invention. (US patent number 7627511.)

An Extension of CreditGrades Model Approach with Levy Process (published in "Quantitative Finance")

Date:Jul. 30, 2008
Author:Takaaki Ozeki⁄Yuji Umezawa⁄Akira Yamazaki⁄Daisuke Yoshikawa

This paper proposes an extended CreditGrades model called the Levy CreditGrades model, which is driven by a Levy process. In this setting, quasi closed-form formulae for pricing equity options on a reference firm and for calculating its survival probabilities are derived.

A Novel Methodology for Credit Portfolio Analysis:
Numerical Approximation Approach

Date:Apr. 24, 2008
Author:Yasushi Takano⁄Jiro Hashiba

This paper proposes a novel numerical methodology for quickly and accurately computing risk measures of a credit portfolio such as VaR(Value at Risk) and CVaR(Conditional Value at Risk), and risk contributions of obligors to these risk measures.

For a brief review of the paper, refer to the following document.

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