Broken Wing Butterfly Price and Volatility - 60/40/20

In the last post, we looked at how the implied volatility (IV) and price of the option strikes in Road Trip Trade (RTT) changed with time. In this post, we'll look at another broken wing butterfly (BWB) strategy, the 60/40/20 BWB. In this strategy, the put options are at 60 delta, 40 delta, and 20 delta. An SPX January 2018 expiration 60/40/20 is modeled below.

(click to enlarge)

As in the last article, we'll use five option chains in our analysis. The options chains we'll use expire on:

• 03-Nov-2017 (7 DTE)
• 10-Nov-2017 (14 DTE)
• 17-Nov-2017 (20 DTE)
• 15-Dec-2017 (48 DTE)
• 19-Jan-2018 (83 DTE)

In the chart below, these five SPX options chains are plotted in terms of IV. In addition, the three strikes of our 60/40/20 along with the current market are marked with vertical lines.

(click to enlarge)

If the market conditions don't change, what can we expect? As time progresses in this trade, we expect the IV of the lower long ("Long 1" - blue vertical line) to increase from approximately 13% to 18+%. Notice how the different expirations move up the blue vertical line ("Long 1") as DTE decrease. The center strike ("Short" - red vertical line), behaves differently, with the IV dropping from approximately 10% to about 8%. The IV of the upper long ("Long 2") first drops from about 8.5% to approximately 7.5%, then increases back to about 8.5%.

So what happens with the price of these put options as DTE decrease? They all lose value with time...not a surprise! The options closer to at-the-money (ATM) lose the most...again, not a surprise. Similar to the IV chart above, the strikes of our 60/40/20 along with the current market price are marked with vertical lines.

(click to enlarge)

As we did with the RTT BWB, we'll use the Black-Scholes model to simulate how the prices of our 60/40/20 strikes change with DTE. For a given strike, we use the actual IVs from our options chains as inputs to the Black-Scholes model.

For the lower long strike of our 60/40/20, the 2450 strike, we have IVs at 7 DTE, 14 DTE, 20 DTE, 48 DTE, and 83 DTE. At 83 DTE the IV of the 2450 strike is 13.3%, and at 7 DTE the IV of the 2450 strike is 18.3%. The chart below shows how the price of the 2450 strike decays with variable IV (changing from 13.3% to 18.3%), with fixed IV of 13.3%, and with fixed IV of 18.3%. The variable IV (purple line) is closer to how this option price will actually decay.

(click to enlarge)

The theoretical decay of the center short strike is shown in the chart below.

(click to enlarge)

Finally, the theoretical decay of the upper long strike is shown in the next chart.

(click to enlarge)

So, how do we expect the price of the entire 60/40/20 to evolve with time? This is shown in ThinkOrSwim (TOS), using four 20 day steps, in the image below. We can see that if the market did not move, and if the IV stayed constant, we would expect the price to increase to expiration. If the market were to drop closer to our center short strike, the profit potential of this trade would increase.

(click to enlarge)

Using the theoretical Black-Scholes option prices from the analysis above, we can model the 60/40/20 price by DTE. Assuming the market and IV remain constant, the Black-Scholes model shows the 60/40/20 price change by DTE in the chart below.

(click to enlarge)

As mentioned in the last article, neither the TOS model or the Black-Scholes model reflect what will actually happen with this trade, even if both the SPX and IV remained constant. These models do provide a view of the general trend of price change with DTE, which can be useful when evaluating your actual trades.

I'll run through a similar analysis of one more BWB structure in the next day or so, before finally finishing up with the Iron Condor backtest analysis.

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