864 Part VI: Measuring and Trading Volatility 
Example: With XYZ at 49, the strategist has the following position in February, so 
that the April calls are nearer to expiration than the July calls. This position is similar 
to a large calendar spread position. 
Option Position 
Position Theta Theta 
Short 4,000 XYZ 0.00 0 
Short 150 XYZ April 50 calls -0.04 +600 
Long 150 XYZ April 30 calls -0.02 -300 
Short 78 XYZ July 30 puts -0.02 +156 
Total Theta: +456 
This position is expected to make $456 per day due to time decay. Note that 
short options, whether puts or calls, have a positive position theta, while long options 
have a negative position theta. A negative position theta means the position has risk 
due to time, while a positive position theta means time is working for the position. 
RHO 
Rho is the name given to the price change of an option's value due to a change in 
interest rates. Recall that one of the components that contributes to an option's price 
is interest rates. As interest rates rise, call prices will rise, but put prices will fall. The 
opposite is true as well: As interest rates fall, call prices decline and put prices rise. 
Rho measures the amount by which these prices rise or fall. 
This behavior of puts and calls with respect to interest rates may not be imme­
diately obvious, but recall that the arbitrage that can be established with in-the­
money calls (the "interest play," discussed in Chapter 27 on arbitrage) demonstrates 
that arbitrageurs are willing to pay more for an in-the-money call as interest rates rise 
because they will be earning more interest on the stock that they sell short against 
that in-the-money call. Thus, rising interest rates cause call prices to increase. 
The opposite is true for puts: Rising interest rates cause put prices to decline. 
Again, an arbitrage can be used to demonstrate the point. Recall that in a reversal 
arbitrage, the arbitrageur is selling the stock and the put while buying the call. We 
have just demonstrated that, as interest rates rise, he is willing to pay more for the 
call since he can earn extra interest on the short sale of his stock. This automatically 
means that he will be willing to sell the put for less. 
Rho is expressed as a positive number for calls and a negative one for puts. Rho 
is smallest for deeply out-of-the-money options and is large for deeply-in-the-money 
options. It is larger for longer-tenn options and is nearly zero for very short-tenn