Quantum option pricing via the Karhunen-Loève expansion
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arXiv
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| Auteurs principaux: | , , , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929244475490304 |
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| author | Prakash, Anupam Sun, Yue Chakrabarti, Shouvanik Che, Charlie Dandapani, Aditi Herman, Dylan Kumar, Niraj Sureshbabu, Shree Hari Wood, Ben Kerenidis, Iordanis Pistoia, Marco |
| author_facet | Prakash, Anupam Sun, Yue Chakrabarti, Shouvanik Che, Charlie Dandapani, Aditi Herman, Dylan Kumar, Niraj Sureshbabu, Shree Hari Wood, Ben Kerenidis, Iordanis Pistoia, Marco |
| contents | We consider the problem of pricing discretely monitored Asian options over $T$ monitoring points where the underlying asset is modeled by a geometric Brownian motion. We provide two quantum algorithms with complexity poly-logarithmic in $T$ and polynomial in $1/ε$, where $ε$ is the additive approximation error. Our algorithms are obtained respectively by using an $O(\log T)$-qubit semi-digital quantum encoding of the Brownian motion that allows for exponentiation of the stochastic process and by analyzing classical Monte Carlo algorithms inspired by the semi-digital encodings. The best quantum algorithm obtained using this approach has complexity $\widetilde{O}(1/ε^{3})$ where the $\widetilde{O}$ suppresses factors poly-logarithmic in $T$ and $1/ε$. The methods proposed in this work generalize to pricing options where the underlying asset price is modeled by a smooth function of a sub-Gaussian process and the payoff is dependent on the weighted time-average of the underlying asset price. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum option pricing via the Karhunen-Loève expansion Prakash, Anupam Sun, Yue Chakrabarti, Shouvanik Che, Charlie Dandapani, Aditi Herman, Dylan Kumar, Niraj Sureshbabu, Shree Hari Wood, Ben Kerenidis, Iordanis Pistoia, Marco Quantum Physics We consider the problem of pricing discretely monitored Asian options over $T$ monitoring points where the underlying asset is modeled by a geometric Brownian motion. We provide two quantum algorithms with complexity poly-logarithmic in $T$ and polynomial in $1/ε$, where $ε$ is the additive approximation error. Our algorithms are obtained respectively by using an $O(\log T)$-qubit semi-digital quantum encoding of the Brownian motion that allows for exponentiation of the stochastic process and by analyzing classical Monte Carlo algorithms inspired by the semi-digital encodings. The best quantum algorithm obtained using this approach has complexity $\widetilde{O}(1/ε^{3})$ where the $\widetilde{O}$ suppresses factors poly-logarithmic in $T$ and $1/ε$. The methods proposed in this work generalize to pricing options where the underlying asset price is modeled by a smooth function of a sub-Gaussian process and the payoff is dependent on the weighted time-average of the underlying asset price. |
| title | Quantum option pricing via the Karhunen-Loève expansion |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.10132 |