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# Accelerate Risk Management in Capital Markets using Quantum Risk Analysis

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Stock markets volatility is commonly associated with investment risk. However, if the risk is effectively managed, it can also generate solid returns for investors. The investment managers and investors acknowledge that they must consider factors other than the expected rate of return for better prediction and decision-making. The decision-making process is filled with uncertainty, with numerous possibilities and probabilities that include a wide range of rewards and risks. There is a way to assist investment managers and investors in making decisions by providing them with a realistic assessment of the risks involved. The Monte Carlo Method, also referred to as Monte Carlo simulation, provides better decision-making in uncertain situations by allowing us to view all the results of our choice and assessing the risk associated. It would be prudent to consider Monte Carlo simulation whenever there are significant number of uncertainties. If not, the predictions may be significantly off, influencing the decisions negatively. Usually, this method will try to sample in line with the probability distribution that illustrates the possible outcomes of an event. Independent samples produced by Monte Carlo simulation might not be appropriate for all problems. Also, the computational requirements of Monte Carlo simulation are the most compelling argument against it. Many capital market use cases that are currently solved using Monte Carlo simulation, such as risk analysis and option pricing, have the potential to be solved faster in time by Quantum Algorithms.

Monte Carlo Simulation and Quantum Algorithm for Risk Management

Monte Carlo method is used to explore the probability space of a single event or a sequence of related events. In Capital Markets, the Value at Risk (VaR - Quantifies the magnitude of potential financial losses over a specific period) and Conditional Value at Risk (CVaR- Quantifies the expected losses that occur beyond the VaR breakpoint) of a portfolio can be determined by using Monte Carlo simulation. This aids in predicting the worst-case scenario for calculating risk given a confidence interval over a given time horizon. However, running these models on a significant amount of data in various dimensions can be computationally expensive. Also, it may be beyond the capabilities of today's classical computers. Here, we will talk about how quantum algorithm on a quantum computer may manage equity portfolio risk, credit risk and currency risk more effectively than Monte Carlo simulation on a classical computer.

Equity Portfolio Risk Management

According to the definition of the Value at Risk and Conditional Value at Risk measures, one may be interested in assessing the likelihood of having a future loss of the given portfolio that exceeds a predetermined value. This entails analysing all possible asset pairings that could default or a large number of conventional samples in a Monte Carlo simulation that requires high computing power to run. This could be greatly sped up in Quantum Computer by algorithms based on Quantum Amplitude Estimation. Amplitude estimation is a quantum algorithm which is used to estimate an unknown parameter which can run faster in time over classical Monte Carlo algorithm. The power of a quantum computer grows exponentially in proportion to the number of qubits linked together. This is one of the reasons why quantum computers may eventually outperform classical computers in risk analysis with high volume of data.

Credit Risk Management

It is critical for Financial Institutions to assess the credit risk of their borrowers in order to meet the Economic Capital Requirement (ECR). Financial institutions that specialise in lending money, referred to in this context as Lenders, evaluate the risk of a loan before approving. Lenders evaluate the risk by determining if the borrower is likely to miss payments. Lenders assess a borrower's current financial position, financial history, collateral, and other criterias to determine how much credit-risky their loan will be. Classical methods of risk calculation are preferred by lenders who are more cautious and risk averse. However, these classical methods are rigid and produce results with only limited number of fixed parameters. Having a 360-degree view of the lender's risk across the entire borrowers group can open new demographics for lending while keeping the risk threshold low. This eventually requires high computing power to calculate the barrowers credit risk and their loan. Unlike the classical Monte Carlo Simulation, the Quantum Amplitude Estimation model can estimate the Conditional Value at Risk with minimal additional overhead and in near real time. The success probability of this algorithm can be quickly increased by repeating the estimation multiple times, which aids in achieving higher accuracy.

Currency Risk Management

The risk of financial impact from fluctuating exchange rates is known as foreign exchange risk or exchange rate risk. Currency risk also affects non-financial enterprises that have receivables or liabilities in a foreign currency. The Value at Risk is being used to calculate the financial reserve and to secure its receivables or liabilities. The Monte Carlo simulation is a simple, easy-to-implement, and flexible to make different assumptions for forecasting an enterprise's currency risk. However, quantum computers can efficiently solve some tasks related to FX reserves management, such as risk measurement using the Quantum Amplitude Estimation model. Compared to classical computers, quantum computers are more prone to errors. To address this difficulty, the process is repeated several thousands of times and the outcome is computed as average of all the results. Running the model with various random variables can improve the accuracy of the expected Value at Risk.

Future Forward

Traditional approaches to enhance Monte Carlo performance rely on importance sampling. However, the problem usually remains difficult in terms of the necessary computing power to solve it in real time. Because of this, the quantum algorithm's potential to boost efficiency in the field of financial risk assessment is particularly compelling. In theory, overnight calculations may be shortened to a shorter time frame, enabling more near real time assessment of risk. The financial institutions would be able to respond to shifting market circumstances and take advantage of trading opportunities faster with such near-real time analysis. Banks primarily utilise Monte Carlo simulation for complex models that can account for uncertainty in variables of a risk analysis. The aforementioned arguments encourage us to consider the quantum algorithmic models. We cannot claim that quantum algorithms are superior to classical algorithms because of the asymptotic tendency of estimation error with respect to calculation time. However, we anticipate that quantum error correction, which uses quantum computation to protect quantum states from errors, is a potential solution to the noise problem, and the Quantum Amplitude Estimation will be superior to conventional Monte Carlo simulations by overcoming these errors. Therefore, the promise of an accelerated quantum speed-up makes it extremely appealing to be one of the first applications to experience a true, practical quantum benefit.