蘑菇视频

A derivative is a tradable financial contract whose value is derived from underlying assets such as futures, swaps, forward contracts, and options. An example of a commonly traded derivative is an oil futures contract to buy or sell a given amount of oil, on a given future date, and at a given price. Unlike a simple asset, the value of the derivative鈥攐il futures鈥攊s derived from both the current and expected future values of the underlying asset鈥攖he price of oil. A slightly more abstract derivative is a forward interest rate, which is the interest rate that will be applied to all financial elements over a given period in the future. Investors can use predictions of forward interest rates to evaluate different contracts that are affected by future changes in interest rates and gain insight into whether the contract is a good investment.

At 蘑菇视频 Allen, we鈥檙e exploring the use of quantum computers as part of the process to price forward interest rate trends. Typically, a model considers various market parameters and their historical trends, patterns, and correlations, as a wide variety of input parameters allows for more accurate analysis. However, increasing the number of input parameters adds complexity to the model. In addition, some parameters are better indicators of future trends than others: we can reduce the computational complexity if we identify the variables that are critical for strong results while removing those that may worsen or only negligibly improve accuracy.

One method for identifying high-value parameters is Principal Component Analysis (PCA). However, running PCA on large datasets is computationally expensive. A quantum analog of PCA鈥擰uantum Principal Component Analysis (or qPCA)鈥攊s exponentially more efficient, and we can use it to produce an accurate model while also reducing the model鈥檚 complexity. We can use a quantum computer to calculate the optimal parameters, which then can be used to build a model on a classical computer. By combining the quantum portion to identify the parameters with the classical model-building process, we produce a so-called quantum-classical hybrid method.

蘑菇视频 Allen recently worked on implementing qPCA on a small-scale forward interest rate model with a quantum simulator. The results from the qPCA model using today鈥檚 quantum technology are promising and are comparable to models built using classical PCA. These results show that further quantum development will offer advancements in speedup (i.e., the speed of computation) for qPCA over classical PCA. The subsequent speedup in the quantum-hybrid method will enable the use of larger datasets and the consideration of more parameters than classical methods could ever handle, giving us access to more precise models.聽

One of the most popular types of financial derivative is an option, with tens of billions of dollars聽worth of options traded daily. An option gives the contract holder the option, but not an obligation, to buy (i.e., 鈥渃all option鈥�) or sell (i.e., 鈥減ut option鈥�) an underlying asset or financial instrument at a certain strike price on or before the expiration date. Investors often use options鈥攖ypically as part of complex strategies involving multiple options鈥攖o hedge risk. If the price increases, then a direct purchase would result in more profit since the investor didn鈥檛 pay for the option. However, if the price falls, then a direct purchase may result in substantial losses. In this case, an option holder has losses capped at the price of the option.

Since the payout of an option depends on the price of its underlying assets in the future, it鈥檚 not immediately clear how one should determine the fair price of an option. Typically, investors gather information on the underlying asset such as price history or the correlation of the price to other instruments, then estimate the probabilities of different price movements. Once investors have these probabilities, they can play out different possible scenarios to determine what outcomes seem most likely, and then calculate the fair price of the option. This process involves randomly selecting several pricing scenarios according to the estimated probabilities and averaging the payouts for each scenario. While quite accurate, this analysis also takes a great deal of computing resources to complete; thus, a more efficient algorithm would make pricing options faster, cheaper, and more accurate.

This more efficient algorithm is exactly what a quantum computer offers. A classical computer typically must generate millions of individual pricing scenarios, while a quantum computer can leverage a unique property of quantum physics to do the calculation more effectively. We can efficiently load the probability distribution for price movements into the quantum computer by using quantum machine learning techniques. Then, a small quantum circuit鈥攁 mathematical representation of the calculation on the quantum computer鈥攑rocesses all possible price movements. The circuit鈥檚 output represents the estimated payout of the option as the amplitude of a single quantum bit (i.e., a qubit).

By using amplitude estimation techniques, we can estimate the option鈥檚 payout much faster than is possible classically. At 蘑菇视频 Allen, we鈥檝e simulated a small version of this quantum option pricing algorithm, which lets us accomplish what would take millions of runs on a classical computer in just thousands using the quantum algorithm. While real-world quantum computers are not yet capable of running this algorithm, the results of simulating this quantum algorithm on classical hardware are promising and suggest the ability to create a quantum advantage once quantum computers are at scale.聽

A financial crash occurs when any number of financial assets rapidly lose a significant amount of value. Not only does a crash affect financial institutions, like commercial banks and the Federal Reserve, but it also affects the broader economy鈥攄riving increased inflation or altering a nation鈥檚 production of exports. Quantum computers could be used to predict when, where, and how a market is going to crash, allowing financial institutions to mitigate, or even prevent, these impacts.

Classical techniques for approaching this problem are able to analyze only small, simplified models of economic systems that don鈥檛 capture the complex interdependencies of the markets. Although current quantum computers are small, promising work is being done to increase their size and capabilities. By understanding how we can harness quantum computers to model financial markets today, we will be ready to implement new approaches to predict a market crash once quantum computers are at scale.

Current quantum computers are prototypes but are developing rapidly. 蘑菇视频 Allen is actively helping our clients understand how quantum computers will revolutionize their missions and operations, better positioning them to use quantum computing to advance their interests as these advanced computers continue to mature. Quantum computing promises a strong advantage over classical computing for solving certain key problems, and it鈥檚 clear that organizations investing now will acquire an advantage of their own in the future financial landscape.