Price an option, or a portfolio of options — vanilla contracts, multi-asset contracts, and path-dependent contracts such as barrier options — on a gate-based quantum computer, in the setting where the paper takes classical Monte Carlo methods as its point of comparison.
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Price an option, or a portfolio of options — vanilla contracts, multi-asset contracts, and path-dependent contracts such as barrier options — on a gate-based quantum computer, in the setting where the paper takes classical Monte Carlo methods as its point of comparison. Stamatopoulos, Egger, Sun, Zoufal, Iten, Shen and Woerner present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, which they describe as an algorithm that provides a quadratic speedup compared to classical Monte Carlo methods. The estimator itself is the subject of this catalog's amplitude-estimation record; what this paper adds is the construction around it on the finance side, and the emphasis it puts on the implementation of the quantum circuits required to build the input states and operators that amplitude estimation needs to price the different option types. The contracts it covers are vanilla options, multi-asset options and path-dependent options such as barrier options. The paper reports simulation results that highlight how the circuits it implements price the different option contracts, and it examines the performance of those option-pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. The authors also report employing a simple error-mitigation scheme that they state significantly reduces the errors arising from noisy two-qubit gates.
Circuit & simulation
problem
encodetransform
algorithm
transformmeasure
readout
measure
What this takes and returns
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
How it works
Stamatopoulos, Egger, Sun, Zoufal, Iten, Shen and Woerner present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, which they describe as an algorithm that provides a quadratic speedup compared to classical Monte Carlo methods. The estimator itself is the subject of this catalog's amplitude-estimation record; what this paper adds is the construction around it on the finance side, and the emphasis it puts on the implementation of the quantum circuits required to build the input states and operators that amplitude estimation needs to price the different option types. The contracts it covers are vanilla options, multi-asset options and path-dependent options such as barrier options. The paper reports simulation results that highlight how the circuits it implements price the different option contracts, and it examines the performance of those option-pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. The authors also report employing a simple error-mitigation scheme that they state significantly reduces the errors arising from noisy two-qubit gates. The Classiq library carries this subject under applications · finance. Reported cost: A quadratic speedup compared to classical Monte Carlo methods, stated in that form and in no other: the abstract attaches the speedup to amplitude estimation itself, and gives no error scaling, no query count, no qubit count and no gate count for the option-pricing circuits, so nothing here says how many samples or oracle calls pricing a given contract to a given accuracy would take, nor at what accuracy the two methods cross over..
Implementation
Unsupported
option-pricing-amplitude-estimation.txt
ALGORITHM: Option pricing by amplitude estimation
PROBLEM: Price an option, or a portfolio of options — vanilla contracts, multi-asset contracts, and path-dependent contracts such as barrier options — on a gate-based quantum computer, in the setting where the paper takes classical Monte Carlo methods as its point of comparison.
IDEA: Stamatopoulos, Egger, Sun, Zoufal, Iten, Shen and Woerner present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, which they describe as an algorithm that provides a quadratic speedup compared to classical Monte Carlo methods. The estimator itself is the subject of this catalog's amplitude-estimation record; what this paper adds is the construction around it on the finance side, and the emphasis it puts on the implementation of the quantum circuits required to build the input states and operators that amplitude estimation needs to price the different option types. The contracts it covers are vanilla options, multi-asset options and path-dependent options such as barrier options. The paper reports simulation results that highlight how the circuits it implements price the different option contracts, and it examines the performance of those option-pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. The authors also report employing a simple error-mitigation scheme that they state significantly reduces the errors arising from noisy two-qubit gates.
REPORTED COST: A quadratic speedup compared to classical Monte Carlo methods, stated in that form and in no other: the abstract attaches the speedup to amplitude estimation itself, and gives no error scaling, no query count, no qubit count and no gate count for the option-pricing circuits, so nothing here says how many samples or oracle calls pricing a given contract to a given accuracy would take, nor at what accuracy the two methods cross over.
BASIS: abstract of arXiv:1905.02666: "We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods." That is the only comparative claim the abstract makes; the rest of it states results rather than bounds — simulation results, a run on the IBM Q Tokyo quantum device, and an error-mitigation scheme — and attaches no figure to any of them. The Classiq index entry this record covers, applications/finance/option_pricing, gives a directory path and a file list and states no bound. Those are the only sources read for this field.
DEMONSTRATED BY: the Classiq library entry applications/finance/option_pricing
PRIMARY SOURCE: Nikitas Stamatopoulos, Daniel J. Egger, Yue Sun, Christa Zoufal, Raban Iten, Ning Shen, Stefan Woerner (2019), Option Pricing using Quantum Computers — https://arxiv.org/abs/1905.02666
This is a literature reference record, not an executable circuit.
A reference record, not runnable source. Leona cannot execute it, so it cannot be saved to your Library as a circuit.
Quantum vs classical
Classical baseline
Compare Amplitude estimation with the strongest classical method for the same instance, input budget, and output metric.
Quantum claim
This reference exposes a quantum circuit pattern; it does not imply an application-level speedup without a matched benchmark.
How to compare
Report input loading, circuit depth, repetitions, classical preprocessing, post-processing, and wall-clock time together.
Declared gaps
Nobody has reviewed this record for gaps yet.
Literature & references
Option Pricing using Quantum Computers2019 · Nikitas Stamatopoulos, Daniel J. Egger, Yue Sun, Christa Zoufal, Raban Iten, Ning Shen, Stefan Woerner
Primary source: it states the methodology for pricing options and portfolios of options on a gate-based quantum computer with amplitude estimation, the quadratic speedup over classical Monte Carlo it attributes to that estimator, the contract types covered (vanilla, multi-asset, and path-dependent such as barrier options), the simulation results, the run on the IBM Q Tokyo quantum device, and the error-mitigation scheme for noisy two-qubit gates. Consult it for the circuits that build the input states and operators, for the accuracies and qubit counts behind the simulations and the hardware run, and for the mitigation scheme itself — the abstract states none of them.