Abstract
Theoretical no-arbitrage option prices are not unique in incomplete markets. This complication stems from the unknown risk-premium, which plays an important role in the option valuation problem. This paper establishes restrictions on the risk-premium parameters. The major tools of this research are the newly derived implications of the stochastic dominance theory applied to option valuation. The presented theory provides no-dominance bounds for option prices. Since the bounds depend on the objective probability measure they lack many risk-premium traits embedded into the options. In the framework of stochastic volatility model, for example, the bounds are independent of the volatility risk premium. This sets limits on both the option values and its risk-premium. Empirical evidence supports this view. Namely, incorporation of the no-dominance bounds in the option valuation in the stochastic volatility model allows to reduce the discrepancy between the market and theory prices by around 15% for options with short maturities both in-sample and out-of-sample.
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