On basic price model and volatility in multiple frequencies

摘要

This paper revisits volatility and emphasizes interrelationships of risk metrics at various time horizons expressed in multiple frequencies. The basic price model defined by Black-Scholes equation and its extensions for varying variance scenarios are presented, i.e. Heston and GARCH models. Moreover, we highlight the significance of abrupt changes in the price of an asset on price modeling and volatility estimation. We extend basic price model where price jumps are taken into account as well. The proposed approach is validated by simulations, and shown that it improves volatility estimation.