The Option Greeks and the Passage of Time

In one of my live interactive meetings with Gold Members at Options for Rookies Premium, we were talking about the passage of time and whether option premium (and thus, bid/ask quotes) were adjusted smoothly with the passage of time or whether they ‘jumped’ each morning as a result of it now being ‘one day later.’ This is a typical (good) question from someone who is new to trading options.

By the way, the answer to the above question is ‘neither.’ Other bloggers, including Mark Sebastian, have discussed this point in detail (Option Pit) , but let me say that market makers have a system for marking the passage of time. My guess is that each uses a proprietary method and that everyone’s timepiece would not read the same time. In simple terms, the ticking clock speeds up as we move from Monday to Friday.

Regardless of the specific details, the people who set the markets accelerate time decay as the end of the week approaches. In other words, the theoretical clock ticks much faster on Friday than on the previous Monday. Why would market makers do this? It’s an attempt to smooth out the passage of time when taking into consideration that the markets are not open for trading on the weekends.

If the option traders used the ‘true’ Friday theoretical values for their bids and offers, when Monday morning arrived each option would (assuming an unchanged sock price) be lower than on Friday. This would be especially obvious as expiration week arrives. To discourage others from ‘dumping’ option premium of Friday and repurchasing Monday, the passage of time used to determine the value of an options is not measured in real time – at least not as weekends approach.

Whether this is a good idea (no markets are open over the weekend) or a bad idea (wars can start over a weekend) is not the point.

That discussion brought us to more questions about how time affects other greeks (in addition to theta). Does delta, gamma, vega change as time passes? The answer is yes, it does. Most of the time, beginners are not introduced to these concepts because they are not important factors on a day to day basis. There are general themes that are important (such as how does delta change as expiration nears), but the details are often overlooked. The math gets complex, but as will all math used in the options world, we have calculators to do the difficult tasks.

With that background, I believe it’s a good idea to introduce you to some of the second order greeks – with the understanding that this is basically a FYI discussion. If you want to get a deeper glimpse into the world of risk measurement when using options (the greeks), read on.

The following is from Wikipedia

Higher-order Greeks

Charm

Charm, or delta decay, measures the instantaneous rate of change of delta over the passage of time. Charm has also been called DdeltaDtime [the rate of change of delta with respect to time]. Charm can be an important Greek to measure/monitor when delta-hedging a position over the weekend. Charm is a second-order derivative of the option value, once to price and once to the passage of time. It is also the derivative of theta with respect to the price of the underlying

Practical use

The mathematical result of the formula for charm is expressed in delta/year. It is often useful to divide this by the number of days per year to arrive at the delta decay per day.

This use is fairly accurate when the time to option expiration is large. When an option nears expiration, charm itself may change quickly, rendering full day estimates inaccurate.

Color

Color, or gamma decay (or DgammaDtime) measures the rate of change of gamma over the passage of time. Color is a third-order derivative of the option value, twice to underlying asset price and once to time.

Color can be important to monitor when maintaining a gamma-hedged portfolio. It can help the trader anticipate the effectiveness of the hedge as time passes.

Practical use

The mathematical result is expressed in gamma/year. It is often useful to divide this by the number of days per year to arrive at the change in gamma per day. This use is fairly accurate when time to expiration is large. When an option nears expiration, color itself may change quickly, rendering full day estimates inaccurate.

DvegaDtime

DvegaDtime, measures the rate of change of vega with respect to the passage of time. DvegaDtime is the second derivative of the value function; once to volatility and once to time.

Practical use

It is common practice to divide the mathematical result of DvegaDtime by 100 times the number of days per year to reduce the value to the percentage change in vega per one day.

There are other 2nd and 3rd order greeks. Today’s discussion is untended to introduce you to the fact that the greeks are all sensitive to the passage of time. And as with the first order greeks with which we are familiar, an approaching expiration date can produce sharp changes in their values.

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