Quantum Computers Poised to Accelerate Complex Derivative Pricing

H Hannan

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Quantum Computers Poised to Accelerate Complex Derivative Pricing
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Quantum computing holds immense potential to revolutionize the pricing of complex financial derivatives like autocallables and target accrual redemption forwards (TARFs). These exotic derivatives depend on an underlying asset’s price movement over time, making them computationally demanding to model.

Classical Monte Carlo simulations struggle to achieve high accuracy for path-dependent derivatives. But quantum algorithms leveraging amplitude estimation promise quadratic speedups over classical approaches. This could drastically reduce compute times from days to seconds.

A new paper by a J.P. Morgan led collaboration details the first comprehensive resource analysis for pricing derivatives on quantum hardware. The researchers introduce a novel “re-parameterization” method to efficiently load stochastic models for asset price distributions. Prior techniques suffered from difficult-to-normalize errors that limited usefulness.

By representing asset paths in terms of log-returns, the team avoids these normalization issues. Pre-trained variational circuits can load discretized normal distributions in parallel to model underlying asset dynamics. An amplitude estimation routine then extracts the expected payoff from the resulting quantum superposition over paths.

The researchers analyzed two popular path-dependent derivatives in detail: auto callables and TARFs. Even for simple instances with 20-30 time steps, they estimate quantum algorithms would need around 8k logical qubits and a logical gate depth of 50 million to demonstrate advantage.

This translates to needing 10 MHz quantum processors resilient to 10 billion operations. While daunting compared to today’s prototypes, this scale appears reachable with future error-corrected quantum devices. Similar resource reductions occurred for Shor’s factoring algorithm through iterative improvements.

The team expresses optimism quantum computing will eventually eclipse classical methods for derivative pricing and other financial use cases. Their approach provides a roadmap for further quantum speedups as better algorithms and hardware emerge. Banks and hedge funds are closely watching quantum advances, recognizing their disruptive economic potential.

DOI: https://arxiv.org/pdf/2012.03819.pdf

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