Security and Derivative Pricing with Fast Regime Switches

Abstract

A regime-switching model lets any parameter of a standard model take a different value in each state of a hidden Markov chain. For the affine and exponential-Lévy models in common use the pricing problem reduces to one linear system, a' = (Q + diag g(t)) a, with the chain's generator Q and a model-specific forcing g as its only ingredients. We expand its solution in the mean holding time of the chain to any order, with an initial layer for the starting regime, and identify the first correction as a Green-Kubo matrix from the group inverse of Q. The same system prices bonds, swaptions, caps, credit default swaps, Asian and digital options, and equity options under stochastic rates, with the Gil-Pelaez integrals conditioned on the regime at expiry where a payoff depends on it; barrier, American and Bermudan instruments go to the coupled equations on a grid. Every numerical claim is checked against QuantLib in the limit where the regimes coincide and against an independent referee with switching on, and the implementation is public.