Chapter 4 - Expiration Profit and Loss

An example of underlying prices and the value at expiration:

After the underlying price of the call goes above 95 it goes up one point in value for each incline because it is worthless otherwise. Vice versa for the put.

Parity Graphs

A parity graph represents the value of an option at expiration, parity being another name for intrinsic value.

Long Call

Short Call

Long Put

Short Put

The slopes of all of these graphs, sometimes called hockey-stick diagrams, are all either -1, 0, or 1 for single options. The slope increases with the number of options bought because if, for example, you bought two contracts the profit (or position value) doubles.

We can combine parity graphs. For instance, say you are long two calls and short an underlying contract. We have the following graph:

Here is the summation of the graph’s slopes, or combined position (looks like an absolute value graph):


This shows that the same option strategy can be constructed in more than one way.

Another larger example:


A table can help us figure out what the combined position should look like:




With the combined graphs it is hard to define a y-axis because they may have different strike prices.

Expiration Profit and Loss (P&L)

Consider a long 100 call at a price of $3.50. We have a parity graph that looks like this:

The author of this text combines several more calls and puts into single graphs as examples far too complicated to replicate, but don’t worry because there will be more to come!

Source:

Natenberg, Sheldon. Option Volatility and Pricing Advanced Trading Strategies and Techniques. 2nd ed., McGraw-Hill Education, 2015.

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