In response to overwhelming demand (Assiduous Reader MW wrote me) I have decided to publish my essay Implied Volatility for FixedResets, which originally appeared as an appendix to the September, 2013, edition of PrefLetter.
The calculator (an Excel Spreadsheet) has been publicly available for some time, linked on the right-hand navigation panel under the heading “Calculators”.
Update, 2016-2-11: An updated and expanded 2016 edition is now available.
Assiduous Reader MW writes in and says:
Also about years, again wondering why you did not use the remaining time to reset (in years) for each issue rather than say 3 years? I am curious about this, because all things being equal would an issue being reset in 1 year not be valued differently than an issue being reset in 4 years?
I have responded:
See page 3 of the essay: “T Years: Column X, calculated data copied from user input. This is the term in years until option exercise and is simply copied from the user input data. It will be noted that in this calculation, T is the same for all instruments, which introduces an error into the calculation – since, of course, Exchange Dates in a set of FixedResets from the same issuer will normally be unique for each issue. I believe that this approximation will have little effect on the calculation compared to the normal vagaries of the market. As the market becomes more efficient, this approximation may have to be reviewed!”
Another reason to keep it constant is to avoid having to invent or estimate a factor that will annualize the Implied Volatility, e.g., if one-year Implied Volatiliity is 5%, what is four-year Implied Volality? It is common to say double, since annualization is often calculated as the square-root of time, but such annualization is highly suspect when we are talking about very lengthy periods, as we are in these calculations.
So I suspect that using actual Exchange Dates and a defined annualization method is simply going to replace one crazy approximation with another. The annualization could be optimized within each calculation to be the x-th root of time, where x is a positive real number, but then there are three factors to optimize, not just two, and I think the quantity of available data will not support this.
However, given the huge variances we are now seeing between current dividend and expected dividend, the proximity of the next Exchange Date is more than it was when I designed the spreadsheet; it may well be that estimating an annualization factor for implied volatility is now the lesser of two evils. I have not yet explored this possibility.
Maybe this should be a contest. I don’t know, I’ll think about it … but maybe if I offer a year of PrefLetter for the best spreadsheet that incorporates actual Exchange Dates and Initial Dividends? Does anybody have any thoughts about this?
I’ve looked at your paper again, and walked through it slowly after reading the website about the Black and Scholes Model http://bradley.bradley.edu/~arr/bsm/pg04.html
Quite complex stuff, with lots of assumptions.
One thing I can’t figure out is Market Spread, and it seems to be quite essential in the calculations. What exactly is your definition of Market Spread?
One thing I can’t figure out is Market Spread, and it seems to be quite essential in the calculations. What exactly is your definition of Market Spread?
This question is addressed in the revised and expanded 2016 edition.
Thanks
Leave a Reply
You must be logged in to post a comment.