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Large-Scale Empirical Tests of the Markov Tree Model

1
Applied Mathematics Unit, University of California, Merced, CA 95343, USA
2
Skytree, Inc., San Jose, CA 95110, USA
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Author to whom correspondence should be addressed.
Academic Editor: Nicholas Apergis
Int. J. Financial Stud. 2015, 3(3), 280-318; https://doi.org/10.3390/ijfs3030280
Received: 29 April 2015 / Revised: 1 July 2015 / Accepted: 14 July 2015 / Published: 27 July 2015
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. View Full-Text
Keywords: option pricing; short-term memory in asset prices; empirical performance; hedging errors option pricing; short-term memory in asset prices; empirical performance; hedging errors
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Bhat, H.S.; Kumar, N. Large-Scale Empirical Tests of the Markov Tree Model. Int. J. Financial Stud. 2015, 3, 280-318.

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