A Quantum Algorithm for Pricing Asian Options on Valuation Trees
Abstract
:1. Introduction
2. Problem and Algorithm
General Idea
3. Quantum Programming
3.1. Qubits
3.2. Quantum Circuits
3.3. Measurement
3.4. Arithmetics with Amplitudes
4. Quantum Algorithm
4.1. Encoding the Paths
4.2. Encoding the Probabilities
4.3. Encoding the Payoff
4.4. Encoding the Positive Part
4.5. Concatenate Circuits and Resulting Computation
4.6. Amplitude Estimation and Quantum Speed-Up
4.7. Dividing the Circuit into Subcircuits to Reduce Depth
5. Results
Application to Binomial Model
6. Discussion
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameters | n | Number of Subcircuits | |||||
---|---|---|---|---|---|---|---|
2 | 3 | 4 | 5 | 6 | |||
(a) | 67 | 141 | 243 | 473 | 847 | 8 | |
Width | 13 | 15 | 16 | 18 | 19 | ||
(b) | 89 | 187 | 337 | 663 | 1229 | 10 | |
Width | 17 | 19 | 20 | 22 | 23 | ||
(c) | 89 | 187 | 337 | 663 | 1229 | 16 | |
Width | 17 | 19 | 20 | 22 | 23 |
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Wolf, M.-O.; Horsky, R.; Koppe, J. A Quantum Algorithm for Pricing Asian Options on Valuation Trees. Risks 2022, 10, 221. https://doi.org/10.3390/risks10120221
Wolf M-O, Horsky R, Koppe J. A Quantum Algorithm for Pricing Asian Options on Valuation Trees. Risks. 2022; 10(12):221. https://doi.org/10.3390/risks10120221
Chicago/Turabian StyleWolf, Mark-Oliver, Roman Horsky, and Jonas Koppe. 2022. "A Quantum Algorithm for Pricing Asian Options on Valuation Trees" Risks 10, no. 12: 221. https://doi.org/10.3390/risks10120221