Abstract
This paper investigates the approximated arbitrage bounds of option prices in an incomplete market setting and draws implications for option pricing and risk management. It gives consideration to periods of global financial crisis and European sovereign debt crisis. To this end, we employ the gain-loss ratio method combined with the market-implied risk-neutral distribution calculated by binomial tree to investigate the options price bounds. Our implied gain-loss bounds of option prices are preference-free and parametric-free to avoid the misspecification error of subjective choice on the benchmark model of gain-loss ratio, and consequently, greatly reduce model risk and market risk. The empirical results show that there are option prices breaking the gain-loss bounds, even after taking into account the market information. This means that a good risk management technique and good-deal investment opportunities exist if the implied binomial tree is used as a benchmark model in the gain-loss bounds.
Highlights
Asset pricing is an essential issue in financial economics
To the best of our knowledge, it is the first attempt to employ the gain-loss ratio method combined with the market-implied risk neutral distribution which is calculated by a binomial tree setting
By employing the gain-loss ratio method combined with the market-implied risk neutral distribution calculated by binomial tree, we reduce the risk of distributional misspecification
Summary
Asset pricing is an essential issue in financial economics. There are two main fundamental ideas that are explored in asset pricing: “equilibrium valuation” and “arbitrage-free valuation”. We use the market-implied distribution to calculate the option benchmark price and build up the gain-loss bounds, instead of using Black-Scholes log-normal assumption, which avoids the pricing errors resulting from the unrealistic assumption and gives a new idea of measuring market risk. To the best of our knowledge, it is the first attempt to employ the gain-loss ratio method combined with the market-implied risk neutral distribution which is calculated by a binomial tree setting. The remainder of this paper is organized as follows: Section 2 presents the model based on a risk-neutral pricing kernel and sets the IBT method that can be employed to derive market-implied probability from the option data.
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