Broken Wing Butterfly Price and Volatility - CDN

In the last two posts (RTT and 60/40/20), we looked at how implied volatility (IV) and price of the option strikes in two broken wing butterfly (BWB) strategies changed with time. In this post, we'll look at another BWB strategy, the centered delta neutral (CDN) BWB. In this strategy, the short put options are at-the-money (ATM), the lower long is at least 100 points below the market, and the upper long is positioned to create a delta neutral structure. An SPX January 2018 expiration CDN is modeled below.

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As in the last two articles, 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 CDN 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 12.5% to 16+%. 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 9% to about 6%. The IV of the upper long ("Long 2") behaves similar to "Long 1" and increases from approximately 8% to about 12%.

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

(click to enlarge)

As we did with the last two BWB strategies, we'll use the Black-Scholes model to simulate how the prices of our CDN 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 CDN, the 2470 strike, we have IVs at 7 DTE, 14 DTE, 20 DTE, 48 DTE, and 83 DTE. At 83 DTE the IV of the 2470 strike is 12.6%, and at 7 DTE the IV of the 2470 strike is 16.1%. The chart below shows how the price of the 2470 strike decays with variable IV (changing from 12.6% to 16.1%), with fixed IV of 12.6%, and with fixed IV of 16.1%. The variable IV (purple line) is closer to how this option price will actually decay.

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

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

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In ThinkOrSwim (TOS), using four 20 day steps, we can see how the price of the CDN changes with time. This is shown 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.

(click to enlarge)

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

(click to enlarge)

Neither the TOS Bjerksund-Stensland model nor 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.

This is all for now for BWB, but in the future we'll look more at how initial conditions impact the outcome of these trades.

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