only a one-month difference between the two options, rho is very small.
Overall, rho is inconsequential to this trade.
There is something curious to note about this trade: the gamma and the
vega. Calendar spreads are the one type of trade where gamma can be
negative while vega is positive, and vice versa. While it appears—at least
on the surface—that Richard wants higher IV, he certainly wants low
realized volatility.
Bed Bath & Beyond January–February 57.50 Put
Calendar
Richard’s position would be similar if he traded the January–February 57.50
put calendar rather than the call calendar. Exhibit 11.4 shows the put
calendar.
EXHIBIT 11.4 Bed Bath & Beyond January–February 57.50 put calendar.
The premium paid for the put spread is 0.75. A huge move in either
direction means a loss. It is about the same gamma/theta trade as the 57.50
call calendar. At expiration, with Bed Bath & Beyond at $57.50 and IV
unchanged, the value of the February put would be 1.45—a 93 percent gain.
The position is almost exactly the same as the call calendar. The biggest
difference is that the rho is negative, but that is immaterial to the trade. As
with the call spread, being short the front-month option means negative
gamma and positive theta; being long the back month means positive vega.