PMC

Comparison of Newton Raphson and Bisection implied volatility with benchmark Black–Scholes implied volatility (dataset-II). Graphs are organized in descending order w.r.t date of maturity

Comparison of Newton Raphson and Bisection implied volatility with benchmark Black–Scholes implied volatility (dataset-I). Graphs are organized in descending order w.r.t date of maturity

MAPK posterior comparisons fltr. (1) posterior inferred from RMHMC sample. (2) Newton Raphson driven RMHMC posterior inferred from sample. (3) posterior inferred from NR-HMC sample (4) exact posterior on a grid. We used a kernel density estimator (kde) to infer densities from samples.

Relative speed for the Simplified Manifold Metropolis-Adjusted Langevin Algorithm (SMMALA) using the same modifications as in the RMHMC code. We calculate the sensitivities using systems of linear equations, we use the sensitivities to obtain the metric and the starting point for the Newton Raphson method which is used to calculate steady states. We tested the relative speed of both the modified and unmodified SMMALA on all three example models with uninformative priors. In all cases, the modified version of SMMALA was faster than the reference implementation.