What Everybody Ought To Know About Options III

Over the past 3 weeks, we have covered option basics including pricing and payoffs. We've also covered Option greeks going deeper into Delta and Gamma last week.

This week, let's take a look at the rest of the greeks : Theta, Rho and Vega.

Theta is the decay of the option premium every day as the amount of time to realize volatility decreases. You can also think of this as the rent paid to own gamma.

The change in the price of an option given a decrease in time to expiration is represented by the greek letter theta. Th

Theta is not the same for al options. With a long time to go before expiration, almost anything is possible. Prices could go very high or very low. As time passes, if we haven't already started to move towards these far away values, the probability of them occurring becomes increasingly small. As a result, options further away from the current asset price decay to zero more slowly than those ATM.

OTM and ITM options have similar decay profiles.
Remember that an ITM call is just parity plus an OTM put.


The value of an asset is also dependent on interest rates determined by the cost of carry of an asset. Rho measures our exposure to interest rates.

The change in the price of an option given a change in the risk-free interest rate is represented by the Greek letter rho r.

If you recall from put-call parity:

Combo = Parity + Carry

Call - Put = (Spot- Strike) + (Interest-Dividends)

Increasing interest rates increases the value of carry

Increasing combo values increases call values and decreases put values

High interest rates increase the value of leverage thereby increasing the value of the combos.


The change in option price for a unit change in volatility is represented by the Greek letter vega. (v)

An option derives its value based on the universe of possible outcomes. The greater the spread of value the underlying could realize, the greater the value of the call option. Volatility is the measure of possible values of the underlying. To calculate this number, we assume that the distribution of stock returns closely follows a normal distribution. Volatility is the standard deviation of these returns.

"Implied volatility" is the expected future volatility of price returns during the term of the option.

Consider that car insurance for a longer period of time costs more than for a shorter period. It makes sense that an increase in risk factors would have a greater effect on a longer-term policy. In our case, the risk factor in question is volatility.

As the duration of an option position increases, so does its vega exposure because it has a greater amount of time to realize a potential spot price movement based on the implied volatility of the market.

The vega of an option position is the measure of exposure to implied volatility. When long options, we are long vega. When short options, we are short vega.

Volatility measures the degree of movement in stock returns over a specific period of time.

-Higher daily moves in the underlying = higher volatility

-Higher implied volatility increases the value of being long gamma

-Higher implied volatility increases the value of an option

-Longer-term options have a greater sensitivity to implied volatility because they have more vega.

Option Values - Rules of Thumb

1. Option premium for ATM options scales with square root of time. So an option of 4x the duration has 2x the value.

2. The implied volatility of an asset is the expected 1-year standard deviation of that asset. The value of a 1-year ATM straddle (long call and long put) is dependent on the expected 1-year standard deviation.

1-year ATM straddle value = Volatility * Spot * 0.8

3. If we double the implied volatility, we double the straddle premium

4. The vega of an ATM option = premium / implied volatility


Comments (4)

Dec 13, 2012

Why do you have Princess Leia and Yoda in the same picture as your thumbnail? Everyone knows they never met, and certainly not on Hoth or any other cold-climate planet.

Dec 14, 2012

Good post. But vega is not a greek letter. It merely pretends to be one.

Dec 14, 2012

OTM and ITM options have similar decay profiles.

Quick correction, FF -> The further OTM you go, the lower the decay, If 20 delta options and 10 delta options decayed at the same rate then the teeny option would soon be priced in a negative.

Otherwise, good post


Dec 15, 2012