The trading strategy for our system will be based on relative value volatility arbitrage as described earlier. This will enable us to trade exclusively with options, to be more precise, in-the-money call options.
First, we define the slope between the two "edges" of the moneyness: the upper and lower bounds of the moneyness. We have to look at a graph for doing this. For the preceding graph, that would typically be [0.5, 1.0].
To get a more mathematical expression for the slope, we look at two points and calculate the slope from these:
Here, m is the moneyness and σ (sigma) is the implied volatility from the option prices. The slope can either rise or fall, which means β will increase, decrease, or of course, neither will happen. Let's look at the two cases more closely.