An Improvement of Gain-Loss Price Bounds on Options Based on Binomial Tree and Market-Implied Risk-Neutral Distribution

Shi-jie Jiang, Mujun Lei and Cheng-Huang Chung
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Shi-jie Jiang: College of Finance and Statistics, Hunan University, No.109, Shijiachong Road, Changsha 410-006, China
Mujun Lei: College of Finance and Statistics, Hunan University, No.109, Shijiachong Road, Changsha 410-006, China
Cheng-Huang Chung: Risk Management Department, Waterland Securities Co., Ltd., 5F., No.188, Sec. 5, Nanjing E. Rd., Songshan Dist., Taipei City 10571, Taiwan

Sustainability, 2018, vol. 10, issue 6, 1-17

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.

Keywords: S&P 500 index options; gain-loss ratio; risk-neutral distribution; binomial tree; risk management (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2018
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