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Estimation of Tail Risk and Moments Using Option Prices with a Novel Pricing Model under a Distorted Lognormal Distribution

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  • Yan Chen
  • Ya Cai
  • Chengli Zheng

Abstract

Risk measures based on the trading option prices in the market are forward-looking, such as VIX. We propose a new method combining distorted lognormal distribution with interpolation to price options accurately and then estimate tail risk. Our method can price the option of any strikes between the maximum and the minimum value of strikes in the real market, which reduces the instability and inaccuracy of using the limited option to measure the risk. In addition, our novel method treats the underlying asset price as a stochastic indicator rather than a fixed indicator as described in previous research studies for risk measurement. Moreover, even if the available sample size is very small, we can measure the risk stably and precisely after interpolation. Finally, the empirical test results of SP500 market show that this method has good performance, especially for the option markets with sparse strikes.

Suggested Citation

  • Yan Chen & Ya Cai & Chengli Zheng, 2020. "Estimation of Tail Risk and Moments Using Option Prices with a Novel Pricing Model under a Distorted Lognormal Distribution," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-25, July.
    • Handle: RePEc:hin:jnlmpe:1603509
    DOI: 10.1155/2020/1603509
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    Cited by:

    1. Hang Lin & Lixin Liu & Zhengjun Zhang, 2023. "Tail Risk Signal Detection through a Novel EGB2 Option Pricing Model," Mathematics, MDPI, vol. 11(14), pages 1-32, July.

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