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We seek to employ the framework of the R package Template Model Builder TMB (Kristensen et al. 2016) which approximately “integrates out” latent variables using the Laplace approximation – to automatically solve the inner problem of the saddlepoint approximation (SPA) and return the negative logarithm of the SPA. All code can be found in this Github repository. The document has the following layout: Introduction to the Laplace approximation Introduction to the Saddlepoint approximation Introduction to TMB Using TMB in numerical SPA calculations and parameter optimization spaTMB example Edit 12.

Four years ago, back in 2014, a friend from HKUST, that had started working in the finance industry, asked me about the VIX. He could not figure out why the CBOE volatility index, popularly called the fear index, was calculated the way it was (see this white paper) – specifically he was curious about the reason for the term \(1/K^2\). Pursuing the quest of understanding the VIX, I remember it felt like very few people truly understood what was going on, and that the ones that did had no interest in sharing their knowledge.