Quantum computing could revolutionize the finance industry, particularly in the area of option pricing. The technology’s potential to speed up computational problems could enhance portfolio optimization, risk management, and option pricing. However, challenges remain, such as preparing a quantum state that encodes a probability distribution of the underlying asset price. A proposed solution involves using Matrix Product State (MPS) as a generative model for time series generation in option pricing. This method could make quantum computing more practicable and speed up option price evaluations. Further research is needed to validate this approach.
What is the Potential of Quantum Computing in Finance?
Quantum computing has been gaining attention in various industries due to its potential to significantly speed up computational problems. One such field that could benefit from quantum computing is finance. Several potential applications have already been considered, including portfolio optimization, risk management, and option pricing.
Option pricing, in particular, is a central problem for financial institutions. An option is a type of derivative, a financial contract in which the option buyer receives a payoff linked to an underlying asset such as a stock, an interest rate index, or a foreign exchange rate. Options offer investors alternative opportunities for profits and hedging various risks. Therefore, it is crucial for financial institutions to price options in a suitable manner to trade and manage them.
Quantum approaches for Monte Carlo-based option pricing have been proposed. The option price is expressed as the expectation of the payoff in a stochastic model of the time evolution of the underlying asset price. Its evaluation can be sped up by Quantum Monte Carlo Integration (QMCI). However, it is unclear whether it would be practicable on real quantum devices due to costly operations such as preparing quantum states that encode probability distributions of the underlying asset price.
How Can Quantum Computing Improve Option Pricing?
One of the challenges in quantum computing for option pricing is preparing a quantum state that encodes a probability distribution of the underlying asset price. This task becomes more demanding when pricing path-dependent options, whose payoff depends on the asset price at multiple dates. In other words, we need to prepare a state encoding the distribution of time series or paths of the asset price.
To reduce the cost of state preparation, alternative methods using no arithmetic circuit have been proposed. Some of these methods use quantum generative modeling. However, there is no previous study on preparing a state encoding the time series distribution via generative modeling in the context of option pricing on a quantum computer.
What is the Proposed Solution for Quantum Computing in Option Pricing?
To address the challenge of preparing a state encoding the time series distribution in option pricing on a quantum computer, a novel approach using Matrix Product State (MPS) as a generative model for time series generation is proposed. MPS, a kind of Tensor Network (TN), was originally developed to represent quantum many-body wave functions efficiently on classical computers. It is a powerful and flexible tool to approximate higher-order tensors as the network of lower-order tensors, thereby reducing the complexity of original tensors.
The MPS-based generative modeling for time series is classically tractable and is strongly related to quantum computing. Given an MPS, we can generate the state on qubits with the corresponding wave function by a quantum circuit in an efficient manner. Therefore, with the aid of MPS, we can find the MPS that generates asset price paths in a given model by a classical computer and then use the corresponding state generation circuit in QMCI.
What are the Implications of the Proposed Solution?
The proposed solution of using MPS as a generative model for time series generation in option pricing on a quantum computer has several implications. First, it provides a new approach to address the challenge of preparing a quantum state that encodes a probability distribution of the underlying asset price. This could potentially make quantum computing for option pricing more practicable on real quantum devices.
Second, the MPS-based generative modeling for time series is classically tractable, which means it can be implemented on classical computers. This could make the transition to quantum computing for option pricing smoother and more feasible.
Finally, the proposed solution could potentially speed up the evaluation of option prices, which is crucial for financial institutions. This could lead to more efficient trading and management of options, thereby benefiting the finance industry as a whole.
What are the Next Steps in Quantum Computing for Option Pricing?
While the proposed solution of using MPS as a generative model for time series generation in option pricing on a quantum computer is promising, further research is needed to validate this approach. Numerical experiments should be conducted to generate time series in the model and demonstrate the capability of the MPS model to generate paths in the model. This would highlight its potential for path-dependent option pricing on quantum computers.
Moreover, more studies should be conducted on preparing a state encoding the time series distribution via generative modeling in the context of option pricing on a quantum computer. This would further advance the field of quantum computing in finance and potentially lead to more efficient and effective financial practices.
In conclusion, quantum computing holds great potential in finance, particularly in option pricing. The proposed solution of using MPS as a generative model for time series generation could potentially make quantum computing for option pricing more practicable on real quantum devices and speed up the evaluation of option prices. However, further research is needed to validate this approach and advance the field of quantum computing in finance.
This article discusses the use of tensor networks in quantum computing for option pricing. The authors, Nozomu Kobayashi, Yoshiyuki Suimon, and Koichi Miyamoto, propose a new method for generating time series data on quantum computers. This method is based on the use of tensor networks, which are mathematical structures that can represent quantum states and operations in a compact and efficient way.
The authors argue that their method can be used to generate time series data for a wide range of financial instruments, including options. This could potentially lead to more accurate and efficient pricing models for these instruments.
The article was published on the arXiv preprint server, which is hosted by Cornell University. This means that it has not yet been peer-reviewed, so its findings should be interpreted with caution. However, it represents an interesting and potentially significant development in the field of quantum computing and finance. You can read the full article at the following link: https://doi.org/10.48550/arxiv.2402.17148.