36 lines
2.4 KiB
Plaintext
36 lines
2.4 KiB
Plaintext
734 Part VI: Measuring and Trading Volatillty
|
||
Opt price = f(Stock price, Strike price, Time, Risk-free rate, Volatility, Dividends)
|
||
Furthermore, suppose that one knows the following information:
|
||
XYZ price: 52
|
||
April 50 call price: 6
|
||
Time remaining to April expiration: 36 days
|
||
Dividends: $0.00
|
||
Risk-free interest rate: 5%
|
||
This information, which is available for every option at any time, simply from an
|
||
option quote, gives us everything except the implied volatility. So what volatility
|
||
would one have to plug in the Black-Scholes model ( or whatever model one is using)
|
||
to make the model give the answer 6 (the current price of the option)? That is, what
|
||
volatility is necessary to solve the equation?
|
||
6 = f(52, 50, 36 days, 5%, Volatility, $0.00)
|
||
Whatever volatility is necessary to make the model yield the current market price (6)
|
||
as its value, is the implied volatility for the XYZ April 50 call. In this case, if you're
|
||
interested, the implied volatility is 75.4%. The actual process of determining implied
|
||
volatility is an iterative one. There is no formula, per se. Rather, one keeps trying var
|
||
ious volatility estimates in the model until the answer is close enough to the market
|
||
value.
|
||
THE VOLATILITY OF VOLATILITY
|
||
In order to discuss the implied volatility of a particular entity - stock, index, or
|
||
futures contract one generally refers to the implied volatility of individual options
|
||
or perhaps the composite implied volatility of the entire option series. This is gener
|
||
ally good enough for strategic comparisons. However, it turns out that there might be
|
||
other ways to consider looking at implied volatility. In paiticular, one might want to
|
||
consider how wide the range of implied volatility is - that is, how volatile the indi
|
||
vidual implied volatility numbers are.
|
||
It is often conventional to talk about the percentile of implied volatility. That is
|
||
a way to rank the current implied volatility reading with past readings for the same
|
||
underlying instrument.
|
||
However, a fairly important ingredient is missing when percentiles are involved.
|
||
One can't really tell if "cheap" options are cheap as a practical matter. That's because
|
||
one doesn't know how tightly packed together the past implied volatility readings are.
|
||
For example, if one were to discover that the entire past range of implied volatility
|
||
for XYZ stretched only from 39% to 45%, then a current reading of 40%, while low, |