Explain asymptotic analysis in interest rate model

Question

Explain asymptotic analysis in interest rate model.

Answer 1

Interest rate model is made tractable through exploiting an asymptotic approximation to the governing equation which is highly exact in practice. The asymptotic analysis simplifies a problem that would otherwise have to be solved numerically. Though, asymptotic analysis has been used in financial problems before, for illustration in modelling transaction costs, it was the first time it actually entered mainstream quantitative financial.