Option Pricing via Quantum Amplitude Estimation

What does a European option actually cost to price with a quantum algorithm, and how does that compare to the classical Monte Carlo method finance normally uses? Every price below is computed live by a real Qiskit quantum-circuit simulation — not a lookup table.

Iterative Amplitude Estimation, Qiskit 3-qubit price grid Cross-checked against Black-Scholes

Option parameters

Spot price and volatility below are made-up numbers until you load a real ticker — they're not tied to any actual stock yet.
What the stock is worth right now
The fixed price you'd be locked into buying (call) or selling (put) at — type an exact value, e.g. half dollars
How much the stock tends to swing around — higher makes the option worth more
How many days until the contract's cutoff date
The standard "safe" interest rate used to discount future money to today's value
Tighter (left) = more accurate, more quantum circuit work
QAE price
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Black-Scholes reference
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closed-form, continuous distribution
Quantum speedup, this run
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Quantum circuit evaluations
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Classical Monte Carlo samples needed
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for the same target precision
Price grid range
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3-qubit discretization of the price distribution
Strike risk
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The price distribution being priced against
This is the actual probability of each possible future stock price, encoded directly onto the quantum circuit's qubits — the thing QAE is computing an average over. With 3 qubits the price range is chopped into 8 discrete levels; the dashed line marks the strike.
Payoff at expiration — if you bought this option today
Profit or loss at expiration for every possible stock price, assuming you paid today's QAE price as the premium. Flat below/above the strike is the premium you paid, fully lost; past breakeven, profit moves dollar-for-dollar with the stock. Hover the chart for the exact number at any stock price. Every dollar figure here re-prices live from the real quantum simulation whenever you change contracts or expiration.
1 contract = 100 shares — scales the dollar figures below, not the per-share price
longer-dated options cost more — this re-runs the real pricing, not just the chart
Max loss
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the premium — 100% of what you paid
Max gain
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Breakeven price
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stock price where profit = $0
Loss zone
Profit zone
Why quantum wins as precision tightens
This chart is precomputed once (not from the sliders above) by sweeping the target precision across two orders of magnitude on a fixed reference option and recording how much work each method actually needed — the same evidence used in the project's full write-up. Both axes are log-scaled, so a shallower line means the cost grows more slowly as precision demands increase.
Classical Monte Carlo (slope ≈ 2)
Quantum amplitude estimation (slope ≈ 1)