<aside> ℹ️ About
</aside>
All the heavy computational lifting is complete.
From here we will use the above tables to compute spreads and reason about what it means to trade vertical spreads and butterflies
<aside> 📣 A word on spread trading in general
Every trade is based on a model of how the world works, even if that model is as basic as “stocks go up on sunny days in Chicago”. Models by definition are simplified representations of how things work.
When we spread trade (buying one instrument and selling a related instrument) we cancel out some amount of model-risk. If our stock valuation model is based on interest rates, when we buy and sell related stocks we are sterilizing the assumptions of the model by letting them offset. Of course, not every stock is equally sensitive to interest rates or whatever parameters our model takes, but the principle of offsetting remains substantial.
In the work you did above, you priced options in an actuarial manner based on an easily computable distribution. In the real world, models such as Black Scholes allow us to price options with continuous distributions and with a set of assumptions about how prices evolve. Everyone knows the assumptions break down in real life but the model’s value is not in its accuracy in absolute terms but as a measure or ruler.
If you have a broken scale, it will not represent your weight accurately but it will still be useful for comparing your weight to mine. How we calibrate a function depends on the use case. Similarly, my guitar can be tuned to itself so that it can reproduce a song pleasantly. But as soon as I start playing with others we need to make sure the group is in tune.
</aside>
<aside> 💡 A word on spread trading in options
An early lesson for options traders is the value of spreads in risk management. I can offset option risks such as exposure to delta, vega, gamma and so on by taking an opposing position in a similar option.
Vertical spreads, where you buy and sell options of different strikes in the same maturity, are terrific examples of this. They allow us to sterilize the impact of bad assumptions in the model itself by reducing the risk to simply distribution. Distributional risks are benign, like over/under bets. The max loss is known and we are insulated from risks like bad interest rate or volatility assumptions.
The closer the strikes are to each other the more the risks offset. As they get further apart the risks increase. We become more vulnerable to discontinuities in our assumptions. Imagine a $100 stock. If I told you that Carl Icahn would make a cash takeover bid of $120 IF the stock dropped below $95 (suppose he knew the board would be far likelier to accept in that scenario) then a naively continuous model would not realize that the 117 strike and 123 strike don’t have a regular relationship to one another. The distribution is not smooth between these points.
The less 2 instruments (or strikes) are related the less insulation you get from model assumptions you get from hedging.
Generally speaking, when we trade narrow vertical spreads or butterflies (which are spreads of spreads — even more insulation) we can say our position is “model-free”. Your risks are more proportional to distributional probability than magnitude which is a more benign circumstance.
</aside>