Thursday, February 25, 2010

Graphing an Option's Evolution

One question I have about risk graphs is why each of the multicolored lines representing different time frames is different?

Thanks for the question Greg. The short answer is time decay. Remember, options are decaying assets and erode in value over time. In addition, the rate of time decay increases exponentially as expiration approaches. Even if all other variables remain constant (ceteris paribus in economic speak) throughout the trade, time decay will incrementally whittle away an option's value. Risk graphs attempt to portray the effect of time decay by showing two different lines: the current and expiration graph. In addition to the two default risk graphs, many software platforms offer the ability to add additional graphs giving you a snapshot of how the trade is expected to evolve between now and expiration. The iron condor risk graph displayed below depicts the profit/loss at various points in time.

[Source: MachTrader]

By viewing the relationship between the different colored lines we can infer if time decay is a benefit to the trade or a detriment. If the lines are rising as time passes (blue to red to green to black), then time is an ally. In greek speak we'd say the position in positive theta. Conversely, if the lines are falling as time passes, then time is an enemy and your position is negative theta.

For related posts, check out:
Theta
Greeks