Abstract
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. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.
Highlights
Options are financial derivative contracts that give the buyer the right, but not the obligation, to buy or sell an underlying asset at an agreed-upon price and timeframe
The advantage of pricing options on a quantum computer comes from the Amplitude Estimation (AE) algorithm [21] which provides a quadratic speed-up over classical Monte Carlo simulations [24, 25]
In the remainder of this section, we focus on QA |0 3, i.e., the outlined algorithm for m = 1, to examine the reach of today’s quantum hardware in evaluating AE option pricing circuits which do not require phase estimation
Summary
Options are financial derivative contracts that give the buyer the right, but not the obligation, to buy (call option) or sell (put option) an underlying asset at an agreed-upon price (strike) and timeframe (exercise window). Developed applications of gate-based quantum computing for use in finance [15] include portfolio optimization [16], the calculation of risk measures [17] and pricing derivatives [18,19,20]. Several of these applications are based on the Amplitude Estimation algorithm [21] which can estimate a parameter with a convergence rate of 1/M , where M is the number of quantum samples used. We employ the maximum likelihood estimation method introduced in [22] to perform amplitude estimation without phase estimation in option pricing using three qubits of a real quantum device
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