# Option gamma time to maturity

In-the-money puts will approach -1 as expiration nears. If options are out-of-the-money, they will approach 0 more rapidly than they would further out in time and stop reacting altogether to movement in the stock. Again, the delta should be about. Of course it is. So delta will increase accordingly, making a dramatic move from.

So as expiration approaches, changes in the stock value will cause more dramatic changes in delta, due to increased or decreased probability of finishing in-the-money. But looking at delta as the probability an option will finish in-the-money is a pretty nifty way to think about it.

As you can see, the price of at-the-money options will change more significantly than the price of in- or out-of-the-money options with the same expiration. Also, the price of near-term at-the-money options will change more significantly than the price of longer-term at-the-money options. So what this talk about gamma boils down to is that the price of near-term at-the-money options will exhibit the most explosive response to price changes in the stock.

But if your forecast is wrong, it can come back to bite you by rapidly lowering your delta. But if your forecast is correct, high gamma is your friend since the value of the option you sold will lose value more rapidly.

Time decay, or theta, is enemy number one for the option buyer. Theta is the amount the price of calls and puts will decrease at least in theory for a one-day change in the time to expiration.

Notice how time value melts away at an accelerated rate as expiration approaches. In the options market, the passage of time is similar to the effect of the hot summer sun on a block of ice.

Check out figure 2. At-the-money options will experience more significant dollar losses over time than in- or out-of-the-money options with the same underlying stock and expiration date. And the bigger the chunk of time value built into the price, the more there is to lose.

Keep in mind that for out-of-the-money options, theta will be lower than it is for at-the-money options. However, the loss may be greater percentage-wise for out-of-the-money options because of the smaller time value. Obviously, as we go further out in time, there will be more time value built into the option contract. Since implied volatility only affects time value, longer-term options will have a higher vega than shorter-term options.

Vega is the amount call and put prices will change, in theory, for a corresponding one-point change in implied volatility.

Typically, as implied volatility increases, the value of options will increase. Vega for this option might be. Now, if you look at a day at-the-money XYZ option, vega might be as high as. Those of you who really get serious about options will eventually get to know this character better. Options involve risk and are not suitable for all investors. For more information, please review the Characteristics and Risks of Standardized Options brochure before you begin trading options.

Options investors may lose the entire amount of their investment in a relatively short period of time. Multiple leg options strategies involve additional risks , and may result in complex tax treatments.

Please consult a tax professional prior to implementing these strategies. Implied volatility represents the consensus of the marketplace as to the future level of stock price volatility or the probability of reaching a specific price point. There is no guarantee that the forecasts of implied volatility or the Greeks will be correct.

Sell long dated and buy short dated options same strike and underlying. Rate of change of option price with respect to the underlying stock.

Variation in delta vs Spot profile for a call option with time to maturity is plotted below: Rate of change of option delta with respect to the underlying stock price. Unlike delta which is bounded between 0 and 1 for a call option and -1 and 0 for a put option, Gamma for a long position in an option can assume any value from 0 to infinity. Gamma is maximum for ATM optiona at expiry. Rate of change of option price with respect to underlying stock volatility. Gamma closer to expiry is higher.

Vega closer to expiry is lower. A variance swap is a forwar contract on realized variance. A physicist thinks reality is an approximation to his equations. A mathematician doesn't care.