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Bid-ask spread, strike prices and risk-neutral densities


  • Xiaoquan Liu


In empirically deriving risk-neutral densities (RNDs) from option prices, one of the key assumptions that the strike prices should be continuous over the entire spectrum of nonnegative real numbers, is not met due to market trading mechanism. This study looks at how this failure affects the empirical RND. It also tests the possible impact that bid-ask spread has on the empirical RNDs. With Heston (1993) option pricing model of stochastic volatility as a mapping tool between option prices and risk-neutral price distributions and realistic assumptions of option specifications, simulation results show that RNDs are less stable and reliable when there are a limited number of different strike prices, even less so when bid-ask spread is incorporated into option prices. Nontechnical Summary Future risk-neutral asset price distributions can be derived from traded options that are written on the asset. In the empirical derivation of these risk-neutral densities (RNDs), some microstructure issues have to be considered. This study looks into the effect of two such issues on the empirical RNDs, the discrete and limited range of exercise prices and the existence of bid-ask spread. The study adopts a simulation-and-testing approach. It assumes that the underlying price distribution follows stochastic volatility and uses Heston's stochastic volatility model for European options as the pricing framework. With specified structural parameters for the Heston model and option specifications, including the current underlying asset price, the time to maturity, the interest rate, it simulates option prices first and tries to infer the assumed asset distribution with different subset of the option prices corresponding to varying number and level of exercise prices. When comparing the original assume RNDs with the empirical RNDs from a subset, we are in a position to detect the influence that discrete and limited range of exercise prices have on the empirical RNDs. Test statistics suggest that RNDs from the lower end of exercise prices deviate most from the original price distribution, especially in the tails. We then perturb the option prices with bid-ask spread. The bid-ask spread is estimated from a model, in which the spread is explained by option characteristics and underlying asset market activities. Statistical tests show that when the bid-ask spread is incorporated into option prices, the derived risk-neutral densities are even less accurate and stable. Therefore, great caution is needed when the empirical densities are used for pricing derivatives, asset market sentiments and so on.

Suggested Citation

  • Xiaoquan Liu, 2007. "Bid-ask spread, strike prices and risk-neutral densities," Applied Financial Economics, Taylor & Francis Journals, vol. 17(11), pages 887-900.
  • Handle: RePEc:taf:apfiec:v:17:y:2007:i:11:p:887-900
    DOI: 10.1080/09603100600829105

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    References listed on IDEAS

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    1. Salazar Celis, Oliver & Liang, Lingzhi & Lemmens, Damiaan & Tempère, Jacques & Cuyt, Annie, 2015. "Determining and benchmarking risk neutral distributions implied from option prices," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 372-387.
    2. Chuang Yuang Lin & Dar Hsin Chen & Chin Yu Tsai, 2011. "The limitation of monotonicity property of option prices: an empirical evidence," Applied Economics, Taylor & Francis Journals, vol. 43(23), pages 3103-3113.
    3. Lina M. Cortés & Javier Perote & Andrés Mora-Valencia, 2017. "Implicit probability distribution for WTI options: The Black Scholes vs. the semi-nonparametric approach," Documentos de Trabajo CIEF 015923, Universidad EAFIT.
    4. Wan-Ni Lai, 2014. "Comparison of methods to estimate option implied risk-neutral densities," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1839-1855, October.

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