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Option Pricing — Quick Recipe

Price a European call option using Quantum Monte Carlo amplitude estimation.

What It Does

Classical Monte Carlo pricing generates random price paths and averages the payoffs. Quantum Monte Carlo achieves the same result with a quadratic speedup using amplitude estimation — O(1/ε) vs O(1/ε²).

This recipe prices a European call option: the right to buy a stock at price K at expiry T, profiting when the stock price exceeds the strike.

Code

from quanta.layer3.monte_carlo import quantum_monte_carlo

result = quantum_monte_carlo(
    distribution="lognormal",
    payoff="european_call",
    params={
        "spot": 100,      # Current stock price ($100)
        "strike": 105,    # Strike price ($105)
        "rate": 0.05,     # Risk-free rate (5%)
        "vol": 0.2,       # Volatility (20%)
        "T": 1.0,         # Time to expiry (1 year)
    },
    n_qubits=5,
)

print(f"Quantum estimate:   {result.estimated_value:.4f}")
print(f"Classical estimate: {result.classical_value:.4f}")
print(f"Grover iterations:  {result.grover_iterations}")
print(f"Confidence:         [{result.confidence_interval[0]:.4f}, {result.confidence_interval[1]:.4f}]")

Expected Output

Quantum estimate:   8.0214
Classical estimate: 8.0213
Grover iterations:  4
Confidence:         [7.8500, 8.1928]

Key insight: The quantum and classical estimates converge, but quantum Monte Carlo reaches this accuracy with quadratically fewer samples on real quantum hardware.

Parameters Explained

Parameter Description Typical Range
spot Current stock price $50–$500
strike Exercise price Near spot price
rate Risk-free interest rate 0.01–0.10
vol Annual volatility (σ) 0.10–0.50
T Time to expiry (years) 0.25–2.0
n_qubits Precision qubits 3–8 (more = more accurate)

Try Next

  • Put options: Change payoff="european_put" to price puts
  • Higher precision: Increase n_qubits=8 for tighter confidence
  • MCP integration: Use monte_carlo_price MCP tool for AI-assisted pricing
  • Volatility surface: Loop over vol=[0.1, 0.2, 0.3, 0.4] to map the surface

See Also