Abstract
The Markov Tree model is a discrete-time option pricing model that accounts for short-term memory of the underlying asset. In this work, we compare the empirical performance of the Markov Tree model against that of the Black-Scholes model and Heston’s stochastic volatility model. Leveraging a total of five years of individual equity and index option data, and using three new methods for fitting the Markov Tree model, we find that the Markov Tree model makes smaller out-of-sample hedging errors than competing models. This comparison includes versions of Markov Tree and Black-Scholes models in which volatilities are strike- and maturity-dependent. Visualizing the errors over time, we find that the Markov Tree model yields more accurate and less risky single instrument hedges than Heston’s stochastic volatility model. A statistical resampling method indicates that the Markov Tree model’s superior hedging performance is due to its robustness with respect to noise in option data.
Highlights
We develop computational bootstrap procedures to better understand how the Markov Tree (MT) model is likely to perform in the future
The results show that the MT model leads to more accurate and less risky hedges
Our primary result is that, when applied to any of these data sets, the three different versions of the MT model described in Section 3.3 all lead to smaller out-of-sample hedging errors than either Heston’s model or the Black-Scholes model
Summary
The Markov Tree (MT) model, introduced in our past work [1,2], is a discrete-time option pricing model that accounts for short-term memory of the underlying asset. Because volatility governs the dynamics of the underlying asset, if we assume it is constant, it should not depend on option parameters such as strike price and expiration date This logic is inconsistent with empirical observations such as the volatility smile. We use market data to conduct extensive tests of the MT model The purpose of these tests is to answer the following central question: which feature is more important to include in an option pricing model, short-term memory of the underlying asset or stochastic volatility? Using one of the established methods for fitting the Heston model, we are able to study the performance of this SV model on a large data set in a reasonable amount of time
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