Implied Volatility in MMGBM model

Abstract

A typical realistic market even if follows a switching GBM, the switching dynamics is in principle unobserved. However, the market price of an option which is a result of bid and ask of a large community may perhaps reflect the accurate state due to the collective knowledge/perception of traders. If that happens, then our computational study shows that it is possible to extract that state information by computing the implied volatility(IV) of at-the-money options. We have also studied the behaviour of IV with respect to time to maturity and also showed that MMGBM model can capture volatility smile for a wide range of market parameters.