Breaking Monte Carlo - Industry Standard Option Model Limits - Implications for Investors and Corporate Finance

Abstract

Pushing models to extremes can expose output biases that stem from underlying assumptions. In the case of industry standard option valuation models, long term, high volatility securities provide a stress test vehicle. For instance, in evaluating a stock with 60% volatility, industry standard option valuation models imply that 69.2% of the stock’s value reflects the likelihood that the share price will rise 600% (septuple) within 10 years. For a portfolio of stocks with 60% volatility, industry standard models project roughly 10% of the holdings will septuple over the course of a decade.

In dealing with high volatility securities over long time periods, do outcomes projected by industry standard option models match up with empirical observations? Or, are the predicted extraordinary returns for a significant percentage of high volatility stocks artifacts of a slant in the models’ foundations?

Do both an assumption of a log normal random distribution of stock prices and the absence of a “reversion to the mean” link to fair value make industry standard option models systematically overweight improbable upside events? Is reported volatility biased upwards when measured under the presumption of a log normal distribution of stock prices, and does that bias in measured volatility also contribute to overweighting improbable upside stock price events?

Considerable discussion has been given to the “black swan” issue (systematic underweighting of improbable events), but the issue here is just the reverse. What are the implications? If widely used option pricing models are systematically skewed to overestimate the likelihood of upside stock price appreciation over long time periods, can investors with superior models find arbitrage opportunities? Are long term executive and employee option packages overvalued with, consequently, excessive expense recognized at grant? Might corporate finance managers find compelling capital strategies that existing pricing models erroneously dismiss?

Keywords: Option pricing model, barrier option, cashless buyback(tm), log normal distribution, option expense recognition

JEL Classification: B23, C15, C21, C22, C24, G12, G13, G31, G32, M41