The theoretical values, in bold type, are those that don’t line up in the
middle of the call and put markets. These values are wrong. The call
theoretical values are too low, and the put theoretical values are too high.
They are the product of an interest rate that is too low being applied to the
model. To generate values that are indicative of market prices, Kyle must
change the interest input to the pricing model to reflect the market’s
expectations of future interest rate changes.
Using new values for the interest rate yields the following new values:
After recalculating, the theoretical values line up in the middle of the call
and put markets. Using higher interest rates for the longer expirations raises
the call values and lowers the put values for these months. These interest
rates were inferred from, or backed out of, the option-market prices by use
of the option-pricing model. In practice, it may take some trial and error to
find the correct interest values to use.
In times of interest rate uncertainty, rho can be an important factor in
determining which strategy to select. When rates are generally expected to
continue to rise or fall over time, they are normally priced in to the options,
as shown in the previous example. When there is no consensus among
analysts and traders, the rates that are priced in may change as economic
data are made available. This can cause a revision of option values. In long-
term options that have higher rhos, this is a bona fide risk. Short-term