Broken Wing Butterfly Price and Volatility - RTT

With SPX implied volatility (IV) so low for months now, and with a strong up trending market, butterflies have been challenging to trade. About the only variations that have been able to withstand both the low IV and uptrend have been broken wing butterflies (BWB). One BWB variation, the Road Trip Trade (RTT) has been reasonably good at handling this market. An SPX January 2018 expiration RTT is modeled below.

(click to enlarge)

Let's look at the options associated with this trade a little more closely. We have several SPX option chains expiring prior to January 2018. We'll choose five to keep the analysis less complicated. The options chains we'll use in our analysis 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 RTT 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 14% to 20+%. Notice how the different expirations move up the blue vertical line ("Long 1") as DTE decrease. We expect the same to occur at the center strike ("Short" - red vertical line), but with a smaller change from approximately 12% to 14+%. The upper long ("Long 2") will change even less, with the IV first dropping before increasing slightly.

If the VIX were to increase, the IV behavior outlined above would remain essentially the same. The magnitudes would change though as the slopes of these IV lines would change.

If the market were to move up, only the behavior of the upper long would change. Rather than the IV of the upper long dropping and then increasing, it would just increase.

If the market were to move up by say 20 points, we can estimate the associated IV change by strike. We can do this by shifting the RTT strikes in the chart down by 20 points. So, 2430 would go down to 2410, and we can see that if the market did not move up any further, the IV of this strike would then change from approximately 14.5% to 22+%. In a similar fashion, we can estimate the IV change of the other two strikes if the market were to move up.

Now, what do these IV changes tell us about the prices of our put options? Well, 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 RTT along with the current market price are marked with vertical lines.

(click to enlarge)

Using the Black-Scholes model we can simulate how the put prices of our RTT strikes will change with DTE. For a given strike, we can use the actual IVs from our options chains as inputs to the Black-Scholes model.

For the lower long strike of our RTT, the 2430 strike, we have IVs at 7 DTE, 14 DTE, 20 DTE, 48 DTE, and 83 DTE. At 83 DTE the IV of the 2430 strike is 13.9%, and at 7 DTE the IV of the 2430 strike is 20.0%. The chart below shows how the price of the 2430 strike decays with variable IV (changing from 13.9% to 20.0%), with fixed IV of 13.9%, and with fixed IV of 20.0%. 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.

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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 RTT 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 through December (gray line), before finally dropping in value into expiration (yellow line). If the market were to drop closer to our center short strike, the profit potential of this trade would clearly increase.

(click to enlarge)

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

(click to enlarge)

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 two more BWB structures in the next few days, before finally finishing up with the Iron Condor backtest analysis.


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