Calibrate the Vasicek short rate model parameters (a, b, sigma) to match an observed zero rate curve. The Vasicek model is dr = a(b - r)dt + sigma dW, where a is mean reversion speed, b is long-term mean rate, and sigma is volatility. This is a fundamental interest rate model used for derivatives pricing, risk management, and scenario generation. The calibration finds parameters that best fit market rates. Used for interest rate derivatives, ALM, and risk analysis.
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Array of zero rates observed in the market
[0.02, 0.025, 0.03, 0.035, 0.04, 0.042]Array of times corresponding to each zero rate
[0.5, 1, 2, 3, 5, 7]Initial guess for mean reversion speed parameter
0.1
Initial guess for long-term mean rate parameter
0.05
Initial guess for volatility parameter
0.01