From the March 2013 issue of Futures Magazine • Subscribe!

Options pricing and delta neutral trades

With its multiple uses, the Log-Log Parabola (LLP) options-pricing model can be a valuable tool for traders interested in a non-theoretical approach to the options market. One application permits the user to see minute-by-minute the options market’s prediction of breakeven underlying prices for profitable delta neutral trades. These are the upper and lower prices at which call and put adjustment trades may be needed. 

The LLP options-pricing model is a Microsoft Excel spreadsheet that permits a number of analytical methods to be applied to options on futures and equities. Input data are any options chain showing the underlying futures or stock price and a set of strike prices with their corresponding options market prices. By using existing prices, the LLP model recognizes that the options market generates a finely tuned set of data on a continuous basis. That is, the LLP does not calculate option prices, but uses listed market prices to produce a regression equation that permits the user to accomplish several types of analysis. These functions include:

  1. Comparing each options market price in an option chain to its expected price on the LLP price curve.
  2. Generating the slope of the options price curve, or delta value, at each strike price.
  3. Showing the height of the options price curve, a measure of relative volatility, at the point at which the underlying asset equals the strike price.
  4. Computing the upper and lower expiration breakeven prices for delta trades — selling options against long futures or equities — at each strike price.

The results generated by the LLP model are based on market price input. Traders in the market forecast future prices and price variability. The LLP takes this information, analyzes it and shows the results.

“LLP: Crude oil, Swiss francs” (below) is the analysis for March 2013 call options on crude oil and Swiss franc futures on Dec. 27, 2012. Twenty strike prices were used with their corresponding options market prices to calculate the regression equations that generate predicted prices, delta values and breakeven prices for delta trades between the calls and March futures contracts. 

Of the 20 strike prices, three are shown in the LLP exhibit. Delta trades based on the LLP values would be based on the slopes of the options price curves at specific strike prices.

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