Examples of nonlinear models
Many nonlinear models have been proposed for academic and applied research to explain certain aspects of economic and financial data that are left unexplained by linear models. The literature on nonlinearity in finance is simply too broad and deep to be adequately explained in this book. In this section, we will just briefly discuss some examples of nonlinear models that we may possibly come across for practical uses: the implied volatility model, Markov-switching model, threshold model, and smooth transition model.
The implied volatility model
Perhaps one of the most widely studied option pricing models is the Black-Scholes-Merton model, or simply the Black-Scholes model in short. A call (put) option is a right, not an obligation, to buy (sell) the underlying security at a particular price and at a particular time. The Black-Scholes model helps determine the fair price of an option with the assumption that returns of the underlying security are normally distributed...
