📈 Black-Scholes 期权定价计算器Black-Scholes Option Pricing Calculator
用 Black-Scholes-Merton 模型计算欧式看涨和看跌期权的理论价格，并给出 d₁、d₂ 及希腊字母 Delta、Gamma、Vega、Theta、Rho；支持连续股息率，并用看涨–看跌平价验算。Price European call and put options with the Black-Scholes-Merton model, with d₁, d₂ and the Greeks Delta, Gamma, Vega, Theta and Rho. A continuous dividend yield is supported, and put–call parity is checked.
使用说明与常见问题How-to & FAQ
「Black-Scholes 期权定价计算器」是什么？What is the Black-Scholes Option Pricing Calculator tool?
用 Black-Scholes-Merton 模型计算欧式看涨和看跌期权的理论价格，并给出 d₁、d₂ 及希腊字母 Delta、Gamma、Vega、Theta、Rho；支持连续股息率，并用看涨–看跌平价验算。Price European call and put options with the Black-Scholes-Merton model, with d₁, d₂ and the Greeks Delta, Gamma, Vega, Theta and Rho. A continuous dividend yield is supported, and put–call parity is checked.
如何使用「Black-Scholes 期权定价计算器」？How do I use the Black-Scholes Option Pricing Calculator tool?
在「Black-Scholes 期权定价计算器」中，填写「标的现价 S」、「行权价 K」、「到期时间 T（年）」、「无风险利率 r（%/年）」、「波动率 σ（%/年）」等参数，结果会随输入实时计算并显示在下方。In the Black-Scholes Option Pricing Calculator: Fill in "Underlying price S", "Strike price K", "Time to expiry T (years)", "Risk-free rate r (% per year)", "Volatility σ (% per year)"; results are recalculated instantly as you type.
Black-Scholes 公式是什么？What is the Black-Scholes formula?
看涨 C = S·e^(−qT)·N(d₁) − K·e^(−rT)·N(d₂)，看跌 P = K·e^(−rT)·N(−d₂) − S·e^(−qT)·N(−d₁)，其中 d₁ = [ln(S/K) + (r − q + σ²/2)T] ÷ (σ√T)，d₂ = d₁ − σ√T，N 是标准正态分布的累积分布函数（这里用 Hart/West 双精度算法计算）。Call C = S·e^(−qT)·N(d₁) − K·e^(−rT)·N(d₂) and put P = K·e^(−rT)·N(−d₂) − S·e^(−qT)·N(−d₁), where d₁ = [ln(S/K) + (r − q + σ²/2)T] ÷ (σ√T), d₂ = d₁ − σ√T, and N is the standard normal CDF (computed here with Hart's double-precision algorithm as given by West).
希腊字母的单位是什么？What units are the Greeks in?
Delta 和 Gamma 按标的价格每变动 1；Vega 按波动率每变动 1 个百分点；Theta 按每过 1 个日历日（年化值 ÷ 365）；Rho 按利率每变动 1 个百分点。Delta and Gamma are per 1 unit change in the underlying price; Vega is per 1 percentage point of volatility; Theta is per calendar day (the annual value ÷ 365); Rho is per 1 percentage point of the interest rate.
模型有哪些假设？What does the model assume?
欧式期权（只能到期行权）、波动率和利率在期内不变、标的价格服从对数正态分布、无交易成本、股息按连续收益率 q 支付。美式期权或离散大额股息需要其他模型。European exercise (only at expiry), constant volatility and interest rate, a lognormally distributed underlying, no transaction costs, and dividends paid as a continuous yield q. American options or large discrete dividends need other models.
计算结果可以作为最终依据吗？Can I rely on the result?
「Black-Scholes 期权定价计算器」按标准公式计算，结果仅供参考；实际金额以银行、券商或税务机关的规则和四舍五入方式为准。The Black-Scholes Option Pricing Calculator uses standard formulas and is for estimation only; actual figures depend on your bank, broker or tax authority's rules and rounding.
「Black-Scholes 期权定价计算器」免费吗？需要注册吗？Is the Black-Scholes Option Pricing Calculator free? Do I need an account?
「Black-Scholes 期权定价计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Black-Scholes Option Pricing Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.