Journal of Investment Strategies

Risk.net

Pricing options using expected profit and loss measures

J. H. Venter and P. J. de Jongh

  • Option traders can get useful information about trade quality by taking expected loss and expected profit as risk and reward measures. Their ratio is especially important.
  • Formulas for European call and put options are derived to implement these measures under the traditional geometric Brownian motion assumption.
  • The notion of option price implied volatility is extended consensus implied volatility for options chains.
  • Optimal portfolios for trading in option chains are introduced and illustrated with practical data.

The pricing of options is discussed, using an approach based on expected profit (EP) and expected loss (EL) as measures of the reward and risk of trades, respectively. It is shown that the EL/EP ratio is an important indicator of the quality of trades. Formulas are derived for these measures for European call and put options under the traditional geometric Brownian motion assumption for the price movement of the underlying security. The Black–Scholes notion of implied volatility is generalized to consensus implied volatility for options chains. Optimal portfolios for trading in option chains are introduced and illustrated with practical data. It is shown that the EPEL approach yields much useful information to option traders.

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