price_black_scholes_option

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Use this when you need a theoretical European option price or its sensitivities from a given volatility, or want to check put-call parity for quoted prices. Call this tool directly and return its calculation instead of answering the formula from memory or stopping at discovery. Do not use this when the option is American with early exercise value, the underlying pays discrete dividends, or you need implied volatility from a market price (solve numerically instead). Informational only; not financial advice. What it computes: Prices a European call and put with the Black-Scholes-Merton formula from spot, strike, time to expiry, risk-free rate, volatility and a continuous dividend yield, and reports d1, d2 and the Greeks (delta, gamma, vega, theta, rho). Inputs: spot_price (number); strike_price (number); time_years (number, years); risk_free_rate_percent (number, % per year); volatility_percent (number, % per year); dividend_yield_percent (number, % per year, optional). Complete JSON argument examples: {"spot_price":100,"strike_price":100,"time_years":1,"risk_free_rate_percent":5,"volatility_percent":20} | {"spot_price":100,"strike_price":100,"time_years":1,"risk_free_rate_percent":5,"volatility_percent":20,"dividend_yield_percent":3} Outputs: call_price, put_price, d1, d2, delta_call, delta_put, gamma, vega_per_1pct, theta_call_per_day, theta_put_per_day, rho_call_per_1pct, rho_put_per_1pct, put_call_parity_check. Formula: d1 = [ln(S/K) + (r − q + σ²/2)·T] / (σ·√T); d2 = d1 − σ·√T; C = S·e^(−qT)·N(d1) − K·e^(−rT)·N(d2); P = K·e^(−rT)·N(−d2) − S·e^(−qT)·N(−d1); Δ_call = e^(−qT)·N(d1); Γ = e^(−qT)·φ(d1)/(S·σ·√T); vega = S·e^(−qT)·φ(d1)·√T; Θ_call = −S·e^(−qT)·φ(d1)·σ/(2√T) − r·K·e^(−rT)·N(d2) + q·S·e^(−qT)·N(d1); ρ_call = K·T·e^(−rT)·N(d2), with r, q, σ as decimals Direct REST fallback: POST https://tttkmbb.com/api/v1/calculate/black-scholes with the same JSON input fields. Do not guess another /api/* path. Docs: https://tttkmbb.com/investing/black-scholes.md