在javascript中计算隐含波动率

// 导入数值计算库
const math = require('mathjs');

// 定义Black-Scholes模型计算函数
function calculateImpliedVolatility(optionPrice, underlyingPrice, strikePrice, timeToMaturity, riskFreeRate) {
  // 使用Black-Scholes公式计算隐含波动率
  const d1 = (Math.log(underlyingPrice / strikePrice) + (riskFreeRate + 0.5 * Math.pow(volatility, 2)) * timeToMaturity) / (volatility * Math.sqrt(timeToMaturity));
  const d2 = d1 - volatility * Math.sqrt(timeToMaturity);

  const callPrice = underlyingPrice * math.norm.cdf(d1) - strikePrice * Math.exp(-riskFreeRate * timeToMaturity) * math.norm.cdf(d2);

  // 使用数值计算库的优化函数，通过迭代计算得到隐含波动率
  const impliedVolatility = math.optimize(function(volatility) {
    const d1 = (Math.log(underlyingPrice / strikePrice) + (riskFreeRate + 0.5 * Math.pow(volatility, 2)) * timeToMaturity) / (volatility * Math.sqrt(timeToMaturity));
    const d2 = d1 - volatility * Math.sqrt(timeToMaturity);

    const calculatedOptionPrice = underlyingPrice * math.norm.cdf(d1) - strikePrice * Math.exp(-riskFreeRate * timeToMaturity) * math.norm.cdf(d2);

    return calculatedOptionPrice - optionPrice;
  }, { method: 'brent' });

  return impliedVolatility;
}

// 调用计算函数
const optionPrice = 5.0;
const underlyingPrice = 100.0;
const strikePrice = 95.0;
const timeToMaturity = 0.5;
const riskFreeRate = 0.05;

const impliedVolatility = calculateImpliedVolatility(optionPrice, underlyingPrice, strikePrice, timeToMaturity, riskFreeRate);
console.log('Implied Volatility:', impliedVolatility);