** **** ***(as published in Active Trader magazine)*

In the last article we started looking at the concept of change and how it affects an option’s fair value. Specifically we used discussed the delta and the gamma – concepts used to quantify the behaviour of an option given a change in the underlying market itself.

In this article, we move a little further down the track and look at how changes in other factors can affect an option. For any option trader, it is interesting information, but more importantly essential in understanding the risk in a position.

In the last issue noted four factors that can impact the fair value of an option position. These are:

- Market price
- Time to expiry
- Volatility
- Interest rates.

Changing levels in the underlying market price is what we looked at last time. Here we will look at the rest, starting with time.

**Time Decay and Theta**

Theta measures the effect of time on an options price.

Let’s look at the Gold futures market, currently trading at $720. Consider buying a 720 Gold call, paying $48. That $48 can be said to represent the chance that the market will go higher and the option move in-the-money.

An option however, has a finite life. As each day passes, the chance of the underlying price reaching the strike and moving beyond it decreases. Therefore the value of the option premium will fall. Even if the Gold futures price stays at $720 exactly, the value of the option will diminish as time passes. This is called time decay.

Do not underestimate the value of understanding time decay. In fact, strategies of many options traders are designed solely to take advantage of time decay.

**The Time Decay Curve**

The actual rate of time decay as each day passes does not stay the same. Assuming all other factors in an options price remain constant (including the underlying price), the rate at which an option premium will decay increases the closer you get to expiry. That is, the option premium will lose more of its value the closer it gets to expiry.

Rather than give a theoretical explanation of this fact, let’s think about it logically. Back with our Gold call, the underlying futures is trading at $720. At the time of writing, a 31 day call with strike of 720 was trading at $48.

Now consider what might happen as time passes. Assuming all other factors remain the same, would you still buy the option tomorrow for $48? What about next week? What about when ti has one week to go? Will it still be worth $48 with say one day to expiry? As time passes, the logical value of the option will diminish.

Remember to think about the price of an option as the odds that the option will finish in-the-money. The reason a 31-day option is priced higher than a 10-day option is the longer life of this option means there is more chance that it will go in-the-money before its expiry date. Simple.

Consider also what happens when one day passes. The 31-day option now has 30-days remaining—it has effectively lost 3.2% of its lifetime (1 day divided by 31). If you have a 10 day option and one day passes, it has lost 10% of its time. Which do you think ** should** lose more in fair value given this one day passing?

Obviously the shorter term option will lose more in value than the longer term option, given the simple fact it has lost more of its life in proportional terms.

If all other factors remain constant, a short-term option will always lose its value at a faster rate than a longer-term option in proportional terms.

· Theta measures time decay. Theta is the rate of change in an option’s theoretical price as one day passes. It is normally expressed in either dollars lost or points lost per day. · As a general rule of thumb, an option will lose 1/3 its time value over the first half of its life, then the remaining 2/3 over the rest of its life. · Like the delta and gamma, the theta for a total position can be calculated by adding each option’s individual theta. This is a relatively simple concept, since theta itself is shown as a dollar or point value. · Strategies that take advantage of time decay are those that have a net short position. Examples are short call, short put, short straddles and strangle and in some cases calendar spread and ratio spreads. · If you are looking at option software, short options give a positive theta and long options give a negative theta. So, to construct a strategy that benefits from time decay, your total theta must be positive. · It is more important to know the concept of time decay than know how to measure theta. |

**When to Place Strategies to Take Advantage of Time**

The important thing to remember when considering a strategy that takes advantage of time decay is that the rate of time decay increases the closer the option gets to expiry.

Therefore, sticking to the shorter-term options means your rate of time decay will be greater (larger theta). Refer again to the time decay curve. The closer the option is to expiry, the faster it loses its value. Therefore, when trading a net short strategy, the shorter the time period, the better.

Traders experienced in selling options understand the underlying market and will only sell options so far out-of-the-money that there is little chance the strike will be reached in the life of the trade. Unfortunately, there is no quick way to learn this. It takes homework and experience. As an options trader, you must understand the key factors that influence the market, both fundamental and technical. Only then can you make an estimate of how far a market can move within a certain time period.

**Volatility and Vega**

The ‘vega’ of an option is a measure of the rate of change in an option’s fair value given a one-percentage point increase in the level of volatility.

The vega is normally expressed as points or dollars gained, given a 1% increase in volatility. The vega for a portfolio is calculated as the sum of the vega for each individual option. An increase in volatility will always have a positive impact on an options price. Therefore, the vega will always be positive. In some texts and software packages, the vega is also known as ‘kappa’ (just to keep you guessing).

** **

· The vega is greatest for options that are at-the-money. This means that a change in volatility tends to impact on at-the-money options more in point or dollar terms than it does in- or out-of-the-money options. · The vega for an option is greater for longer-dated options. This means that a change in volatility will have a greater impact on options that have a longer time to expiry. · The vega for an at-the-money option is relatively constant across different levels of volatility. |

** **

**Interest Rates and Rho**

The ‘rho’ measures the sensitivity of an option, given a change in interest rates. The interest rate component of an option’s price is associated with the cost of carry and is not normally a significant component. In fact, most traders pay little attention to the rho.

· The rho for options on leveraged instruments is set to zero, since there is a very marginal cost of carry. · For stock options, calls will have a positive rho and puts will have a negative rho. A positive rho means an increase in interest rates and this will have a positive impact on the options price. A negative rho has a negative impact. |

**So where do you start?**

If you are not new to options, but new to the concept of these Greek symbols, should you be calculating your delta, gamma, theta, vega and rho for all your position all of the time?

You could guess that things could get a little messy.

Suffice to say you should be aware they exist and you should at least know how to interpret them. Additionally it is worth knowing how these measurements apply to positions that involve more than one option.

If at any point, any of the ‘Greeks’ get a little confusing, you remember all these measurements do only one thing. They help you understand how the profit and loss of an option position will react to a change in a certain variable. These are measurements of risk. *Understand your risk.*