Derivative Model Applications

Abstract

The Black–Scholes GBM (geometric Brownian motion) model can be generalized to other models that are more realistic for particular markets. The various simple extensions to the Black–Scholes model assume constant parameters for ease of calculation. In reality, the properties of time series such as volatility, mean reversion, long-term levels and jump behaviour will at the very least vary through time with reasonably predictable patterns. These characteristics can be included in spot models.