Option contracts are a type of financial derivative that allow investors to
hedge risk and speculate on the variation of an asset's future market price. In
short, an option has a particular payout that is based on the market price for
an asset on a given date in the future. In 1973, Black and Scholes proposed a
valuation model for options that essentially estimates the tail risk of the
asset price under the assumption that the price will fluctuate according to
geometric Brownian motion.
We describe an automated method for computing rigorous lower bounds for
topological entropy which was originally introduced in [Day et al., 2008]. We
combine this method with the work of Zin Arai in [Arai, 2007] to find rigorous
lower bounds on topological entropy for 43 hyperbolic plateaus of the H\'enon
map. We also examine 15 area-preserving plateaus and compare our results with
related work.