期权定价计算器
完整希腊值的Black-Scholes期权定价
期权定价计算器输入
$
标的股票的当前市场价格（例如：150）
$
期权可以行权的价格（例如：155）
到期前的天数（例如：30）
%
年化无风险利率（例如：5代表5%）
%
股票年化隐含波动率（例如：25代表25%）
此计算器使用1973年开发的Black-Scholes模型。提供欧式期权的理论公允价值。
C = S·N(d₁) − K·e^(−rT)·N(d₂)
Delta (Δ): 期权价格相对于股价的变化率。Delta为0.60意味着股票每变动1美元，期权变动0.60美元。
Gamma (Γ): Delta相对于股价的变化率。高Gamma意味着Delta变化迅速。
Vega (ν): 期权价格对隐含波动率1%变化的敏感度。
Theta (Θ): 时间衰减——期权价格每天减少的金额。期权在接近到期时失去价值。
Rho (ρ): 期权价格对无风险利率1%变化的敏感度。通常对短期期权影响最小。
什么是Black-Scholes期权定价模型？
Black-Scholes模型是为欧式期权合约定价的数学框架。1973年发表，革命性地改变了金融市场。
模型接受五个输入并为看涨和看跌期权生成理论价格。
Black-Scholes公式
C = S·N(d₁) − K·e^(−rT)·N(d₂)
d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T)
该公式将期权价格计算为预期股价与行权价现值之差。
看跌期权的公式通过看涨-看跌平价推导。平价确保价格内部一致。
理解隐含波动率
隐含波动率（IV）是市场对股票未来价格波动的预测。与回顾性的历史波动率不同，IV是前瞻性的。
交易者经常将IV与历史波动率进行比较，以评估期权是便宜还是昂贵。
Black-Scholes模型的局限性
模型假设恒定波动率和利率、对数正态分布、无股息、无交易成本和仅欧式行权。
尽管有这些限制，Black-Scholes仍是最广泛使用的起点。从业者会调整股息并使用二叉树模型。
期权定价计算器常见问题
隐含波动率在大多数期权交易平台上可用。在期权链中查找IV列。
Black-Scholes严格为欧式期权定价。对于不支付股息的美式看涨期权，价格相同。
Delta有三个实际含义：(1)每1美元股价变动的预期期权价格变化，(2)期权到期实值的近似概率，(3)等效股票头寸。
Common Options Strategies: Covered Calls, Cash Secured Puts & Iron Condors
The Black-Scholes calculator above prices individual options, but most traders deploy structured strategies that combine multiple legs. A covered call involves owning 100 shares of stock and selling a call option against them — generating premium income in exchange for capping your upside. The Black-Scholes price tells you the fair value of the call you are selling, helping you identify overpriced options that offer better income potential. A covered call calculator uses the same pricing inputs to estimate your net cost basis and annualised return.
A cash secured put involves selling a put option while holding enough cash to buy the shares if assigned. This strategy generates premium income and can be used to acquire stocks at a lower effective price. A cash secured put calculator uses implied volatility and time decay (Theta) to assess whether the premium adequately compensates for the assignment risk. Theta — the rate at which an option loses value as expiration approaches — works in your favour when selling options.
An iron condor combines a bull put spread with a bear call spread — selling one put and one call while buying a further out-of-the-money put and call to cap maximum loss. Iron condors profit when the stock stays within a defined range and implied volatility is elevated. An iron condor calculator uses the Black-Scholes prices of all four legs to compute the net credit received, the maximum gain and loss, and the breakeven prices. This strategy is popular during earnings seasons when IV is high and large price moves are uncertain.
The option greeks calculator output above is central to all these strategies. Delta tells you the directional exposure of each leg. Gamma shows how fast Delta changes as the stock moves. Theta quantifies the daily time decay you earn as a seller or pay as a buyer. Vega measures sensitivity to changes in implied volatility — critical for strategies that are long or short volatility. Rho, the sensitivity to interest rate changes, matters most for long-dated options.
