Here is a section of content that I have written and have yet to write much more. I do not know what the final structure of the amalgamation of my research over the years would be, whether that would take shape in an ebook, an educational manual, or just many more posts in my blog. This blog has served as a personal journal of my interests in the financial markets and in volatility. Perhaps it is time I start to engage more with those that visit this site. I would highly appreciate any feedback you could provide. Thank you.
Fair
Volatility (VIX) Estimate Model & Indicator 8-19-13
After the financial crisis of 2008, I believed
the market structure had changed significantly and new models—or at least the
discarding of previous rules--were needed to generate a trading “edge”. So, I designed Fair Volatility (VIX)
Estimate Model & FVE Indicator in May 2010. Trading VIX Derivatives and VIX Exchange Traded Products seemed
like the ideal assets class to utilize my trading experiences from both the
directional and volatility trading worlds.
VIX is calculated
from a weighted average of implied volatilities from options prices of multiple
strikes on the S&P500 Index with a constant maturity of 30 days to
expiration. For example, a VIX number
of 15 technically reflects the option market participants’ expectation that the
S&P 500 Index would move within a ~4.33% range up or down (with confidence
of one standard deviation or 68%), within a one-month time frame. Because VIX represents an annualized volatility
number, we need to divide 15 by the square root of 12 (months in a year) in
order to come up with a one-month equivalent number.
In reality, however,
VIX reflects the market’s expectation of price volatility, fluctuation AND
behavior of the S&P500 Index looking 30-days into the future.
S&P500 Index options are bought as insurance to protect
against potential decline in the value of equity portfolios. Obviously, the higher the demand, higher the
value of protection and thus higher VIX levels. This is why VIX is commonly referred to as the “Fear Index”. It is well known that VIX usually moves in
opposite direction as the S&P500 Index.
This inverse correlation is seen 70 – 80% of the time. Therefore, in building a VIX model, we
should look at more than just volatility.
VIX is a function of Volatility Factor & “Fear”
Factor.
 |
| Chart of FVE & VIX 8-19-13 |
 |
| FVE Trading Simulation on Front Month VIX Futures 8-16-13 |
Based in options theory, it is my understanding that the
core component of any volatility model is a way to efficiently calculate
realized volatility, otherwise known as historical volatility or statistical
volatility. I prefer the term “realized
volatility” because there is a strategy in options volatility trading known as
gamma scalping, which is a form of volatility arbitrage
In gamma scalping, one would buy for example the options straddle
of an underlying stock or index and then at certain price or time intervals hedge
the delta exposure of the options straddle by buying or selling the underlying
instrument. Let me explain this process
in greater detail.
For example, let us say you bought 100 September straddles (long Sep 37 call, long Sep 37 put,
each 100 contracts) for the combined price of 2.25 and implied volatility of
24% on XXX stock. This straddle
purchase would cost you $22,500. Now
let us also imagine an extreme case that XXX stock price for the next one-month
period remains unchanged on a day-to-day closing price of 37. In this case, at expiration, you would lose the
entire $22,500 by holding the straddle as it expires completely worthless
However, let us also
assume in this extreme example that intraday, XXX stock price fluctuates up or
down by $1 and back to the closing price of 37. Let us also assume that you hedge your delta exposure of the
straddle by buying and selling XXX stock as the price fluctuates intraday. If the gamma on the 37 strike options is
0.14, then with XXX stock $1 lower to 36 intraday, the delta of the calls would
change from +0.50 to +0.36, and the delta of the puts would change from –0.50
to –0.64. The new net delta of the straddle
with stock price at $36 would have changed to -0.28 from zero. On an options position of 100 straddles, this
would mean buying 2800 shares (-0.28 * 100 straddles * 100 unit shares/per
option) of XXX stock at the price of 36 to bring the net delta exposure to zero. Finally, as the price of XXX stock moves
back to 37 by market close, you would sell the 2800 shares that were bought at
XXX stock price of 36 in order to bring the net delta exposure back to zero. On the flip side, if the stock moves up from
37 to 38 intraday, then you would short sell 2800 shares of XXX stock at 38 to hedge
the new delta exposure of the straddle of +0.28. Once again, as the stock price closes at 37, you would buy back
the 2800 shares stock sold short at 38.
This is a simplistic
and unrealistic example which does not account for the change in gamma over
time as well as execution costs. However,
if you were to repeat this process each and every day for 21 trading days or
one month time frame, you would have lost the entire $22,500 you paid for the
options straddle but profited $58,800 from the delta hedging process of buying
and selling stock for a net profit of $36,300!
This is where the
term “realized volatility” comes from. A $1 price fluctuation intraday of a $37 stock is equivalent to a
42.9% volatility (1/37 * square root of 252-- # of trading days per year). Remember that the September 37 straddle was
bought at 24% implied volatility. The
rule in any profitable trading is to buy/sell lower/higher and sell/buy higher/lower. In gamma scalping, one is buying/selling
implied volatility of options and selling/buying by capturing or “realizing”
stock volatility.
Let us take a look at an example of selling implied
volatility or selling 100 straddles using the same scenario as above, except that instead of $1, XXX stock
is assumed to fluctuate just $0.30 intraday.
To hedge the delta exposure with stock price at 36.70 and 37.30, you
would buy and sell 840 shares of XXX stock.
The net result would be $22,500 profit from options less $5,292 from
delta hedging process for a net profit of $17,208. A $0.30 price fluctuation on a 37 stock price is equivalent to a
12.9% realized volatility. In this
reverse example, one would have sold 24% implied volatility and bought at a
12.9% realized volatility.
Volatility arbitrage is the main reason why implied
volatility and realized volatility move hand in hand. If they did not, then there would be tremendous opportunities to
buy or sell implied volatility against stock volatility. The most important and critical challenge,
however, in deciding whether to buy or sell volatility is to determine future
volatility of the underlying instrument.
Ah, of course! The future is
unknown and uncertain.
However, volatility I believe is actually more predictable
than the price direction of a stock. Think
of volatility as a volt meter. We know
from physical reality, that energy moves back and forth from high intensity to
low intensity, unlike stock prices which could continue to move up or down.
There are several ways to measure a stock’s price
volatility. Historical volatility of
closing prices is the simplest & most widely known. The following lists other more efficient
ways.
1)
Historical volatility: close to close
2)
Exponentially Weighted
3)
Parkinson: High to Low
4)
Garman-Klass: Open/High/Low/Close
5)
Rogers-Satchell: Open/High/Low/Close
6)
Yang-Zhang: Open/High/Low/Close
7)
GARCH & EGARCH models[1]
8)
Average True Range[2]
9)
My “Realized Volatility” calculation
The following report provides an excellent summary of the
various ways to measuring historical volatility from 1 – 6 in the above list--(http://www.todaysgroep.nl/media/236846/measuring_historic_volatility.pdf.
GARCH models are also widely looked at as a way to predict
future volatility. The Average True
Range indicator is widely used in technical analysis, but seldom mentioned in
volatility modeling circles.
When designing my “Realized Volatility” measure, I wanted
something that was both simple and usable.
I analyzed my own delta hedging actions while I was an options market
maker and came up with the following formula.
Realized Volatility = 11 trading day exponential moving
average of [If (Absolute Value(Log(High/Prior Close))>Absolute Value(Log(Low/Prior
Close)), then Absolute Value(Log(High/Prior Close))*square root(252), else Absolute
Value(Log(Low/Prior Close))*square root(252))*Adjustment Factor].
Basically, I look at how much the market pushes the price up
or down from the prior closing price and translate this into an annualized volatility
measure. Then I take the 11-day exponential
moving average of those values to come up with my Realized Volatility
calculation. The adjustment factor can
be 0.80 – 1.00, depending on the longer-term implied volatility levels of the
underlying instrument. This Realized
Volatility measure does not take into account the general rise in implied
volatility levels prior to earnings announcements or other events, therefore, should
not be applied to stocks, except for periods prior to one month before and 2 weeks after
such events. It is appropriate for
indices, commodities and sector ETFs. The
adjustment factor also serves as a tool to use if I want to have a bias of
being short or long options, in general, but this adjustment factor makes this
measure a tool and not necessarily a theoretical model.
Here is what the Realized Volatility indicator looks (blue),
compared to VIX (black) and the traditional historical volatility measure
11-days (green), & the FVE indicator (red).
