Journal of Risk

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Delta-hedged gains and risk-neutral moments

Sol Kim and Dahea Kim

  • The risk premium incorporated in option prices has changed going through several market crashes.
  • Delta-hedged option gains are negatively associated with skewness and kurtosis among call options, but positively associated with the higher moments among put options. 
  • Investors pay premium for call options in anticipation of a positive jump, while they pay premium for put options in anticipation of a negative jump. 

ABSTRACT

We investigate the well-documented underperformance of delta-hedged option portfolios in relation to ex ante moments of the stock market's return distribution. Using a sample of Standard and Poor's 500 index options, we find that delta-hedged option gains decrease with ex ante volatility, in support of a negative volatility risk premium. Moreover, the delta-hedged gains are negatively associated with skewness and kurtosis of call options, but positively associated with the higher moments of put options. These results suggest that investors pay a premium for call options in anticipation of a positive jump, while they pay a premium for put options in anticipation of a negative jump.

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