Extended Model of Stock Price Behaviour

Abstract

We have developed an extended model for stock price behaviour that is able to accommodate fat-tailed distributions with support as large as [ ] , −∞ ∞ . The "homogeneously saturated" (HS) model avoids exponential price changes for large fluctuations by means of a saturation parameter. In the limit where the saturation parameter is zero, the standard model of stock price behaviour (i.e., geometric Brownian motion) is recovered. We compare simulated stock price series generated for both the standard and HS model for the DJIA and five random stocks from the NYSE and NASDAQ exchanges. We find that in all cases, the HS model provides a better fit to the observed price series than the standard model. This has implications to many areas of finance including the Black-Scholes formula for option pricing.

Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time

“…Fat-tailed distributions of returns ground the observed phenomenon. The distributions were discovered in the stock market (Jondeau and Rockinger 2003;Koning et al 2018;Rachev et al 2005), in the Forex (FX) (Cotter 2005;Dacorogna et al 2001), as well as in Bitcoin, prices (Begušić et al 2018;Liu et al 2017). The fat tails, accompanied by the extensive discontinuity of the price curve (jumps), make the equally spaced time intervals inconvenient for high-frequency market analysis.…”