# How Theta Changes

Traders need to understand how thetas change because the impact of time erosion on option prices will directly affect trading strategies. Surprisingly,traders frequently misunderstand or oversimplify this concept,usually with unfortunate results. A word of warning: Theta, the estimate of the impact of time on option values, is preceded by a
minus sign, which can be confusing when discussing “biggest” and“smallest” values.

Read this section carefully! Table 4-7 and Figure 4-10 show that thetas are smallest (the highest absolute value) when options are at the money. The differences show up more clearly in the figure than they do in the table because, on an absolute level, the numbers seem small, between 0.00 and 0.05. Also, even though rows E and F of Table 4-7 reflect thetas at their smallest (highest absolute value) when the 100 Call and 100 Put are at the money, the differences are not obvious because the numbers are rounded to two decimal places.

At-the-money options have larger time values than in-the-money or out-of-the-money options, and it is the time-value portion of an option’s price that erodes. Therefore,given the same amount of time to expiration, at-the-money options lose more value per unit of time than in-the-money or out-of-themoney options.Thetas and Time to Expiration:Tables 4-7 and 4-8 and Figure 4-11B show that thetas of at-the-money options decrease (increase in absolute value) as expiration approaches.

Thetas of at-the-money options are smallest (largest absolute value) during the last unit of time prior to expiration. In row E of Table 4-7, in which the stock price is 100, the theta of the 100 Call starts at 0.05 (column 1) and then decreases to 0.06, 0.07, and 0.09 before going to zero at expiration.Table 4-7 and Figures 4-11A and 4-11C show that thetas of in-themoney and out-of-the-money options behave differently than thetas of at-the-money options.

They get smaller (absolute value increases) for a while, but then they get larger (absolute value decreases) as expiration approaches. Because thetas behave differently for in-the-money,at-the-money, and out-of-the-money options, traders must be careful when making generalizations about the impact of time decay on option values.Using Theta with Delta How does a trader use theta? Since theta estimates how much a position will make or lose over

some period of time, a trader buying options can use theta in conjunction with delta to estimate how much the underlying stock price must change in price in a specific time period for the delta effect (price movement of the underlying) to make more than the theta effect (time decay). Assume, for example, that an option has a one-day theta of 0.05 and a delta of 0.35. The buyer of this option therefore needs a \$1.00 price rise in the stock in seven

days to offset the time erosion—the delta effect of 0.35 will offset the theta effect of seven times 0.05. Although market forecasting is an art, not a science, having a time period and a price target give the trader a frame of reference on which to base a subjective trading decision. Thetas and Volatility Table 4-8 and Figures 4-12A, 4-12B, and 4-12C show that thetas of inthe-money, at-the-money, and out-of-the-money options decrease (increase in absolute value)

as volatility increases. This result is logical because an increase in volatility increases option values. And, given the same time to expiration, a higher option value contains more time erosion per unit of time.How Rho Changes:Rho estimates how much an option value changes when the interest rate changes and other factors remain constant.Rho is generally of least concern to option traders because rhos are small in absolute terms and because interest rates

generally do not change dramatically, that is, more that 1 percent, in a short period of time. Nevertheless, traders need to learn four rules about how rhos change. The first rule is that rhos of calls are positive and rhos of puts are negative. This is a result of the cost-of-carry concept explained in Chapter 6, where the conversion strategy is discussed.With rising interest rates, the cost to finance a stock position increases.As a result, the time value of a call

must increase relative to the time value of the put. Therefore, if interest rates rise while stock prices and put prices remain constant, then call prices must increase to pay for the increased financing costs. Rhos of calls therefore are positive.Similarly, if interest rates rise while stock prices and call prices remain constant, then put prices must decrease so that the put-call time-premium differential increases enough to pay for the increased financing costs. Rhos of puts therefore are negative. In reality, neither a call nor a put remains constant while the other changes.