Charlie LaiinStackademicPricing VIX options using the Heston modelThis study prices VIX options using the Heston model, utilizing the VVIX Index and derived formulas for efficient parameter calibration.Jun 301Jun 301
Charlie LaiinStackademicHow the VIX WorksThe Volatility Index, commonly called VIX, is a real-time market index representing the market’s expectation of 30-day forward-looking volApr 15Apr 15
Charlie LaiinStackademicPricing Zero-Coupon Bonds by the Vasicek Interest Rate ModelThis article aims to use the Vasicek model to price bond prices and use Python to achieve this task.Jan 21Jan 21
Charlie LaiinStackademicUsing Real-World Data to Calibrate the Vasicek Interest Rate Model with PythonThe Vasicek model, introduced in 1977, was the initial model to incorporate the mean reversion characteristic of interest rates, a feature…Jan 171Jan 171
Charlie LaiTransform Black-Scholes PDE to Heat Equation Step by Step.The Black-Scholes equation and the heat equation are two different partial differential equations (PDEs) used in different contexts. Let me…Nov 4, 2023Nov 4, 2023
Charlie LaiWhy Do We Call the Maximum Likelihood Estimation Using “Likelihood”, Not “Probability” directly?In statistical inference, the likelihood function plays a pivotal role, enabling data to furnish insights regarding a statistical model…Oct 14, 2023Oct 14, 2023
Charlie LaiinStackademicThe Real Meaning of the Historical Volatility FormulaVolatility is an important risk metric to measure the uncertainty of a stock price. The most common method to calculate volatility is using…Oct 8, 2023Oct 8, 2023
Charlie LaiLinear Regression is the Best Prediction when (X, Y) Obeys Bivariate Normal DistributionLinear regression is simple, intuitive, and explainable, with fewer assumptions and theoretical support. However, if we know that…Oct 1, 2023Oct 1, 2023
Charlie LaiProbability Density Function is Not a ProbabilityIn this article, I’d like to explain why a probability density function(pdf) is not a probability. In fact, a probability density function…Sep 24, 2023Sep 24, 2023