On the entropy minimal martingale measure in the exponential Ornstein-Uhlenbeck stochastic volatility model
This paper derives, analyzes, and simulates the minimal entropy equivalent martingale measure for an exponential Ornstein-Uhlenbeck stochastic volatility model.
What it examines
This paper examines how financial markets price options using an entropy-minimal martingale measure. It employs the exponential Ornstein-Uhlenbeck model to address incomplete markets where standard replication fails. The study reviews theory and develops a variational principle-based method for option pricing.
What it concludes
The paper derives an explicit entropy-minimal martingale measure using the Hobson construction for an exponential Ornstein-Uhlenbeck volatility model. This approach enhances option pricing in incomplete markets. Potential applications include improved option valuation, risk management, and model calibration for derivative securities.
Evidence objects
Researchers Kabanov and Sonin derive an explicit formula for the minimal entropy equivalent martingale measure by employing sophisticated stochastic differential equations and the Hobson construction in an exponential Ornstein--Uhlenbeck model.
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Empirical simulations using Monte Carlo methods with Euler schemes validate the model on real market data including stocks such as GOOG, demonstrating accurate option pricing predictions despite inherent market uncertainties.
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Despite theoretical breakthroughs and practical validation, the study acknowledges simplifying assumptions like constant parameters and idealized market conditions, urging further research to expand entropy minimization techniques for broader financial applications.
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Demonstrating rigorous mathematical derivation, this paper uniquely obtains the entropy minimal martingale measure for the exponential Ornstein--Uhlenbeck model, addressing option pricing challenges in incomplete markets. Although it builds on established frameworks (\$Hobson\$, \$Frittelli\$, and others), its precise treatment and innovative technical insight render it compelling for modern quantitative finance research.
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Raw abstract and provenance
Abstract: We consider a stochastic volatility model where the price evolution depend on the exponential of the Ornstein--Uhlenbeck process. After a brief revision of the related theory the entropy-minimal equivalent martingale measure. is calculated. We consider a stochastic volatility model where the price evolution depend on the exponential of the Ornstein--Uhlenbeck process. After a brief revision of the related theory the entropy-minimal equivalent martingale measure. is calculated. △ Less
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