Quantum Finance

Quantum Wave Option Pricer

Price European call options using a Schrödinger-type wave mechanics model. Explore the interference correction to Black-Scholes and compute the novel Greeks Ξ, Φ and κ — as derived in From de Broglie Waves to Option Pricing.

C_Q = (w₁² + w₂²) · C_BS + C_int | C_int = 2w₁w₂ e^−rT · 𝒞 · Re[e^iφ(S₀e^μ¯TN(d₁)−KN(d₂))]

Parameters live update

Market

Spot Price S₀100

Strike K110

Risk-free Rate r3.5%

Maturity T0.50 yr

Volatility σ25.0%

Wave Mechanics

Packet Width σ₀0.100

Planck Const. ℏ_f0.150

Wave Number 1 k₁3.00

Wave Number 2 k₂-1.50

Weight w₁ √0.60.775

Phase φ₀0.300

Δk = 4.50 σ_eff = — Coherence 𝒞 = — Moneyness = ATM

Quantum Price C_Q

—

Wave mechanics model

Black-Scholes C_BS

—

Classical component

Interference C_int

—

Quantum correction

Coherence 𝒞

—

e^{−½Δk²σ_eff²}

Greeks & Novel Sensitivities

Delta

—

BS: —

Gamma

—

BS: —

Vega

—

BS: —

Theta

—

BS: —

Planck Greek

—

∂C/∂ℏ_f

Phase Greek

—

∂C/∂φ₀

Coherence Greek

—

∂C/∂k₁

Ξ, Φ, κ are novel Greeks
unique to the wave model

Implied volatility across strikes — the smile emerges from the oscillatory interference correction C_int

Price decomposition C_Q = C_BS + C_int across spot prices, with intrinsic value for reference

Delta profile — quantum oscillations around Δ_BS due to the interference term

Gamma profile — convexity Γ_Q vs Γ_BS across spot prices; quantum interference amplifies curvature near the strike

Vega profile — volatility sensitivity ν_Q vs ν_BS across spot prices; decoherence can produce negative vega in the interference term

Theta profile — time decay Θ_Q vs Θ_BS across spot prices; phase drift creates non-monotone decay patterns

Novel quantum Greeks across spot prices — Ξ (Planck: ∂C/∂ℏ_f), Φ (Phase: ∂C/∂φ₀), κ (Coherence: ∂C/∂k₁) — sensitivities unique to the wave model