import * as math from 'mathjs';
export const normalCDF = (x) => {
const t = 1 / (1 + 0.2316419 * Math.abs(x));
const d = 0.3989423 * Math.exp(-x * x / 2);
const p = d * t * (0.319381530 + t * (-0.356563782 + t * (1.781477937 + t * (-1.821255978 + t * 1.330274429))));
return x >= 0 ? 1 - p : p;
};
export const normalPDF = (x) => {
return (1 / Math.sqrt(2 * Math.PI)) * Math.exp(-0.5 * x * x);
};
export const blackScholes = (S, K, T, r, sigma, optionType = 'call') => {
if (S <= 0 || K <= 0 || T <= 0 || sigma <= 0) {
throw new Error('S, K, T, and sigma must be positive');
}
try {
const d1 = (Math.log(S / K) + (r + 0.5 * sigma * sigma) * T) / (sigma * Math.sqrt(T));
const d2 = d1 - sigma * Math.sqrt(T);
if (optionType === 'call') {
return S * normalCDF(d1) - K * Math.exp(-r * T) * normalCDF(d2);
} else if (optionType === 'put') {
return K * Math.exp(-r * T) * normalCDF(-d2) - S * normalCDF(-d1);
} else {
throw new Error('Invalid option type. Must be "call" or "put".');
}
} catch (e) {
throw new Error(`Black-Scholes error: ${e.message}`);
}
};
export const optionGreeks = (S, K, T, r, sigma, optionType = 'call') => {
if (S <= 0 || K <= 0 || T <= 0 || sigma <= 0) {
throw new Error('S, K, T, and sigma must be positive');
}
try {
const d1 = (Math.log(S / K) + (r + 0.5 * sigma * sigma) * T) / (sigma * Math.sqrt(T));
const d2 = d1 - sigma * Math.sqrt(T);
let delta, gamma, vega, theta, rho;
if (optionType === 'call') {
delta = normalCDF(d1);
gamma = normalPDF(d1) / (S * sigma * Math.sqrt(T));
vega = S * normalPDF(d1) * Math.sqrt(T);
theta = -(S * normalPDF(d1) * sigma) / (2 * Math.sqrt(T)) -
r * K * Math.exp(-r * T) * normalCDF(d2);
rho = K * T * Math.exp(-r * T) * normalCDF(d2);
} else if (optionType === 'put') {
delta = normalCDF(d1) - 1;
gamma = normalPDF(d1) / (S * sigma * Math.sqrt(T));
vega = S * normalPDF(d1) * Math.sqrt(T);
theta = -(S * normalPDF(d1) * sigma) / (2 * Math.sqrt(T)) +
r * K * Math.exp(-r * T) * normalCDF(-d2);
rho = -K * T * Math.exp(-r * T) * normalCDF(-d2);
} else {
throw new Error('Invalid option type. Must be "call" or "put".');
}
return { delta, gamma, vega, theta, rho };
} catch (e) {
throw new Error(`Option Greeks error: ${e.message}`);
}
};
export const sharpeRatio = (returns, riskFreeRate = 0) => {
if (returns.length < 2) throw new Error('Need at least two return values');
const avgReturn = math.mean(returns);
const stdDev = math.std(returns);
if (stdDev === 0) return 0;
return (avgReturn - riskFreeRate) / stdDev;
};
export const valueAtRisk = (returns, confidence = 0.95) => {
if (returns.length < 10) throw new Error('Need more data for VaR calculation');
const sortedReturns = [...returns].sort((a, b) => a - b);
const index = Math.floor((1 - confidence) * sortedReturns.length);
return -sortedReturns[index];
};
export const cashflowSchedule = (principal, rate, periods, compounds = 1) => {
const schedule = [];
const periodicRate = rate / compounds;
let balance = principal;
for (let i = 1; i <= periods; i++) {
const interest = balance * periodicRate;
balance += interest;
schedule.push({ period: i, interest, balance });
}
return schedule;
};
