Adaptive wave model for financial option pricing is proposed, as a high-complexity alternative to the standard Black--Scholes model. The new option-pricing model, representing a controlled Brownian motion, includes two wave-type approaches: nonlinear and quantum, both based on (adaptive form of) the Schrodinger equation. The nonlinear approach comes in two flavors: (i) for the case of constant volatility, it is defined by a single adaptive nonlinear Schrodinger (NLS) equation, while for the case of stochastic volatility, it is defined by an adaptive Manakov system of two coupled NLS equations. The linear quantum approach is defined in terms of de Broglies plane waves and free-particle Schrodinger equation. In this approach, financial variables have quantum-mechanical interpretation and satisfy the Heisenberg-type uncertainty relations. Both models are capable of successful fitting of the Black--Scholes data, as well as defining Greeks. Keywords: Black--Scholes option pricing, adaptive nonlinear Schrodinger equation, adaptive Manakov system, quantum-mechanical option pricing, market-heat potential PACS: 89.65.Gh, 05.45.Yv, 03.65.Ge
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