Options Trading Strategies | Implied Volatility & Probability


Option's Anatomy

The anatomy of an option's value is made up of 6 elements with the corresponding "Greek" measuring the sensitivity/exposure to that specific element:

1.  Underlying instrument's Price.  Delta & Gamma (& Lambda).

2.  Time to Expiration remaining.  Theta.  

3.  Implied Volatility.  Vega (not a "Greek", a.k.a Kappa).

4.  Short-term interest rate.  Rho.

     ❑ 3 Month (90 Day) T–bill is the default rate.

5.  Strike price of the option (ITM, ATM and OTM).  Mix of Greeks specific to strike.

6.  Dividends (if relevant).  No directly corresponding Greek(s).

Both Time to Expiration and Volatility have a DIRECT impact on the option's value 

❑  More Time to Expiration makes both calls and puts rise in value. 

❑  Less Time to Expiration makes both calls and puts fall in value.

❑  Higher volatility makes both calls and puts rise in value. 

❑  Lower volatility makes both calls and puts fall in value.


The product's Price itself has its own varying impact on calls distinct from puts, for e.g.

❑  As price rises, straight calls increase in value; but, puts decrease in value.

❑  As price falls, straight calls decrease in value; but, puts increase in value.

Interest Rates and Dividends (if relevant) have opposite effects on calls versus puts

❑  As Interest Rates rise, long calls rise in value; but, long puts decrease in value.

❑  As Interest Rates rise, short calls decrease in value; but, short puts rise in value.

❑  As Interest Rates fall, long calls decrease in value; but, long puts rise in value.

❑  As Interest Rates fall, short calls rise in value; but, short puts decrease in value.

❑  As a company raises its Dividend, long calls decrease in value; but, long puts increase in value.

❑  As a company raises its Dividend, short calls rise in value; but, short puts decrease in value.

❑  As a company lowers its Dividend, long calls increase in value; but, long puts decrease in value.

❑  As a company lowers its Dividend, short calls decrease in value; but, short puts rise in value.


Listed options have no right to the dividend. The options just reflect what the product's price is expected to do. As a Dividend is raised, the drop in price will be more, once the underlying goes ex-dividend. This makes calls decrease in value; but puts increase in value.  As a Dividend is lowered, the drop in price will be less once the underlying goes ex–dividend. This makes calls increase in value; but, puts decrease in value.

❑ You may choose to trade European-style Indexes that are absent of dividends, to remove dividends out of the equation from the start.

Direct and opposing effects explain why calls and puts do not share identical values at their common ITM, ATM and OTM strikes. Calls and Puts shift between asymmetrical distribution curves, losing their symmetry – remember at any given strike there will always be a pairing of an OTM Call with an ITM Put, an ITM Put is paired off with an OTM Call, and an ATM/NTM Call is paired up with an ATM/NTM Put. Paired does not mean one is an identical twin of the other.

Which elements impacting an option's anatomy do you not have the choice of accepting or rejecting, when structuring a chosen option spread? 

❑  Federal Open Market Committee determines Interest Rate policy. Not your say.

❑  Dividend policy is decided by the listed company.  Not your say.

❑  Price of the underlying product is market–driven. Not your say.


Quote: “Of a stock’s move ...  

❑  31% can be attributed to the general stock market, 

❑  13% to industry influence, 

❑  36% to influence of other groupings, and the remaining 

❑  20% is peculiar to the one stock.”

Benjamin F. King, Market and Industry Factors, Journal of Business, Jan–1966.

So, which elements of an option's anatomy is left for you to decide on?  Strikes, Time to Expiration & Volatility.  As Time is Synthetic Volatility and Volatility is Synthetic Time, for which both are unique to an option's strike, at minimum, 50% of your trading day's effort must focus on Volatility analysis.

Strikes

The exchange on which the product is traded decides the number of strikes and increments between strikes. For retail traders, to control the risks within limits due to smaller sized accounts, it is advisable to choose products with

❑  $1 wide increments between strikes for Calendars. Maximum width would be a product with $2.50 increments between strikes. 

❑  $1 to $2.50 wide increments between strikes for Verticals, maximum of $5.

Are you too wide or slim? Not your waistline. But, are you exposing short positions to too much credit margin at risk for a given strike width; and, you construct long positions that are too cramped without room for the debit to expand? Reconfigure the strike width.

Time to Expiration

You decide how much time to sell and buy. Advisable for retail traders to be

❑  Short Net Credit spreads between 30–50 days with an ROI of between 1%–2% per day at minimum, at maximum 3%–4% per day.

❑  Long Net Debit Spreads between 60–90 days up to a maximum of 120 days, with an ROI range between 150%–200+% within 60 days of being in the trade, is considered a reasonable expectation.

Volatility – Debating Historical versus Implied & Which Options Pricing Model Applies?

Much debate surrounds comparing both Implied Volatility (IV) and Historical/Statistical Volatility (HV/SV) against each other.  While IV and HV are meant to converge at an option's expiration, it is not certain that convergence will occur.  Why? Various combinations of corporate action (e.g. takeovers/investigations), or variance in earnings guidance may prevent an assumed "over/underpriced" option reaching convergence at expiry.  Moreover, you cannot re–simulate the macro–economic parameters affecting the volatility specific to an Asset Class.  The Home Options Trading process has chosen to remove the use of Historical Volatility altogether.  HV–IV cross–over signals only cause visual confusion: no such cross–over signals were used as trade entry criteria in generating the Consistent Results shown in the model portfolio.

IV is a forward looking estimate, which explains why there are back/far month expiration intervals.  So, for practical trading purposes, it makes sense to forecast IV 30-120 days forward.  There is no reason  to look backwards, as you cannot Theoretically Price Historical Volatility into the option/spread you plan to be long/short in.

– Of note, Vega measures the amount of change in the option price for a 1% change in Implied Volatility (not HV/SV).  There is no "Greek" that measures HV/SV.

Here's the key difference between Historical Volatility and Implied Volatility.

❑  HV is an annualized standard deviation of price changes expressed as a %.  

It calculates how volatile the underlying was for X. number of past trading days (adjustable period), prior to each observation date in the data series, for that given  period. For HV you can adjust the period to be different from the option's expiration cycle; but not with IV – the expiration cycle is fixed. 

– HV measures how fast the underlying has been moving around in the past for that given period.  HV is not a substitute for IV.  HV of an underlying may have benign volatility behavior in the past but become extremely active suddenly, with nothing to anticipate this change in activity.  Especially with volatility, history fails to predict future expectations based on past experiences.

– Rather than rely on HV, it's more meaningful to look at Gamma, as how fast (acceleration) or how slow (deceleration) it can manufacture positive/negative Deltas to propel/stabilise your position.  A HV measure of "fast" is not needed, as  you can view Deltas live each trading day in your platform, as the "Speed or Rate of Change" + Gamma as "Acceleration/Deceleration".  Also, remember Theta is the cost of embedding that Acceleration/Deceleration in your Deltas, given the Gamma–Theta inverse relationship.  Theta is the expense for pushing the pedal to the metal.

           

❑  IV is the collective forward estimate (forecast) of participants trading that underlying of its standard deviation of daily % changes in price from the present, until the option expires.  In the anatomy of an option's value, it is IV that needs attention.

– Prices of an option's premium is entered into an options pricing model, to  solve for IV.  Depending on which of the 3 most commonly used Theoretical Pricing Models used, the IV value is computed using various algorithmic combinations, typically using both ATM/Nearest–The–Money Calls and Puts.

– It is the IV (not HV) of an option that is the required standard deviation input when entered into a pricing model that makes an option's current Theoretical Price equal to the current market price. When you price to enter or exit trades for a particular day, you use the current spot prices to Theoretically price the intrinsic/extrinsic value of the ITM/ATM/OTM strikes of a spread's construction, not a historical number.

❑  The volatility variable is the only unobservable parameter in an option's pricing model. It is termed a "variable" parameter as volatility is not fixed but rises/falls to extreme levels; then, reverts to its mean, or is repulsed away from its mean.  There are upper and lower limits within which IV is contained or breaks out of.

❑ The option price, the futures price, time to expiration, interest rate and strike price(s) are all observable (i.e. known/measurable). So, these known parameters can be entered into specific fields in most trading platforms, to  solve for the only unknown parameter – volatility. As volatility is derived from known parameters that is why it is called "Implied" Volatility.

In practice, what this means is to evaluate IV levels (Low, Medium or High in % terms) first, then Probability. Finally, reconcile both pieces of analysis using the Reward:Risk Ratio of the underlying's PRICE (with and without analysis of changing dates to simulate Theta as decay bought/premium sold separately), to accept/reject the opportunity as an economically viable trade.

Now, let's look at probability.  Delving into the intricacies of the maths of options pricing models is not for everyone.  Still, you must know which of the 3 Options Pricing Models: Bjerksund–Stensland, Binomial and Black–Scholes, matches the Exercise Style (American or European) of the underlying product you are trading. It affects the outcome of your probability analysis.

❑  Some may dismiss minor probability differences in constructing constrained Delta (&  Gamma) range–bound strategies like Iron Condors and Calendars.

Calendars require a separate treatment of probability.  But, for highly break–even sensitive strategies like a Straddle/Strangle or Ratio Backspreads that must break out of a range to be profitable, using a consistent model to be precise with the Probability of Touching specific strikes is critical.  While these strategies cited are all indifferent to direction, you need to reconcile the chosen strategy with the relevant probability model.

Models – Humps & Curves ... Probability Distribution, Skew & Kurtosis that is!

With any of the 3 Options Pricing Models, all have a common feature – a Distribution Curve.

There are 4 measures associated with the Distribution Curve. These 4 measures in math–speak are called "moments", a concept originated from physics expressing quantity.  A moment represents the magnitude of force, measuring distance from an axis of rotation.  
As a retail trader, do not get hung up about the math–speak; but, understand how the mechanics of these 4 measures apply to the Distribution Curve of the Option Pricing Model you select in the trading screen. Taken all together, these 4 moments express the probability distribution of your constructed spread in relation to the underlying product traded.
4 Moments
1. The Mode of the probability distribution of X, where X is the underlying's price.
Measures of central tendency ('"averages"): Mean, Mode and Median can be used to describe what price could behaviourally do in a certain way around the live price itself. 
Most trading platforms use the "Mode" in their distribution curve to calculate probability, as it's the most widely–accepted central tendency measure for trading purposes.  Back to basic statistics ... 
❑  Mode is the most frequently occurring value in a data series.  The number of occurrences at a price point expressed as a probability is useful for trading.  The order gets filled as price occurs at a particular point.
❑  Median is the value in a data series, where half the values are higher than it and half the values are lower than it.  It doesn't help traders with the frequency of price occurring.
❑  Mean is calculated by adding all values in the data series, then dividing it by the number of values in the data series.  It is not an observable number in itself, as it derived from other numbers.  To see the impact of price movements on your option trade, there is no use in expressing probability with mean numbers, as it is composed of other numbers. 

2. Variance, is expressed as a positive or negative interval away from the mean.  
The square root of which is the Standard Deviation (SD) or Standard Error, also referred to as the "Probability Range".  Most trading platforms have a +/– σ symbol ("sigma") representing the SD, with a Probability Range field that can be set to 1σ (68%), 2σ (95%) & 3σ (99%).
  
3. Skew, is the measure of the shift ("lopsidedness") in the density of the probabilities of a distribution curve, as the Mean–Median–Mode separate from each other and are no longer equal to one another.  See "Distribution Types: Normal, Positive & Negative Skew".

 

Skews exist for the very reason that institutions are taking on/laying off the risks in their underlying positions against that market they are trading in (a.k.a "hedging").  Skews arise from institutional hedging needs and their requirement to limit unexpected arbitrage in the market(s) they are exposed to.  

❑  To hedge, institutions use large amounts of Calls and Puts in varying quantities and combinations, in turn affecting the supply and demand for options (ITM, ATM & OTM), reflected in changes of the underlying's Put-Call Ratio.


A retail trader may say ... I typically only use ATM and OTM options, so what has Institutions taking ITM positions have to do with me? 

❑  Always remember at a given strike, there is an ITM Call/Put paired with an OTM Put/Call at that SAME strike. So, as Institutions drive Supply/Demand for ITM Calls/ITM Puts impacting the IV, on the flip side, your OTM Puts/OTM Calls get affected. ATM/NTM options are not exempt from this Supply/Demand action either, as they sit between ITM and OTM options. 

Only when there is no skew (skew = 0), is the Supply/Demand of Calls exactly equal to the Supply/Demand of Puts. Precise equilibrium of the fear of price rising matches off exactly against the fear of price rising.  Perfect equilibrium is unlikely to last (a few seconds maybe; but, not over days).  Especially in highly liquid Index/ETF products, there is an inherent skew bias in the underlying. And zero skew conditions do not remain, as Supply/Demand of Puts/Calls must become imbalanced at some point, to create a two–sided market with Bid–Ask differentials.

Other than a Zero Skew, there are 3 other types of Skews:

❑  Positive Skew: As strike prices increase, Implied Volatility of both Calls & Puts rises higher. 
– Most prevalent in Agricultural Commodities (Corn, Wheat, Soybeans, Bean oil, meal), Orange juice, Coffee and Oil/Oil products.
❑  Negative Skew: As strike prices increase, Implied Volatility of both Calls & Puts falls lower.
– Most prevalent in equity Indexes: S&P, OEX (XEO), bonds and livestock (cattle).
❑  Dual Skew: product has both Positive and Negative skews, typically the skew reverses around the Near-the-Money strikes or ATM.
– Most prevalent in Gold, Silver, Metals and Currencies/Currency ETFs.
Look on the right pagelets for examples of how to use Positive, Negative and Dual Skews.


4. Kurtosis, measures whether the distribution is tall and thin or short and flat, compared to the normal distribution of the same variance, around the Mode (the Live Price of the underlying traded).  It suggests when and which options are over/underpriced.
❑  A Normal Distribution curve has Zero Kurtosis.
❑  Positive Kurtosis (Leptokurtic) has 
– A pointed peak around the live price of the distribution = higher probability or greater frequency than a normal distribution of future price occurrences to be closer to the live price; and
– "Narrow shoulders" = higher probability or greater frequency than a normal distribution for price occurrences to have extreme moves within 1, 2 or 3 Standard Deviations, as the body of the Leptokurtic midsection is narrower than a normal distribution.
– Narrower midsection = lower probability or less frequency of intermediate moves compared to a normal distribution.
– Positive Kurtosis suggests OTM Calls & OTM Puts and ITM Calls & ITM Puts are underpriced.
❑  Negative Kurtosis (Platykurtic) has 
– A flatter rounder peak around the live price of the distribution = lower probability or less frequency than a normal distribution of future price occurrences to be closer to the live price; and,
– "Wider shoulders" = lower probability or less frequency than a normal distribution for price occurrences to have extreme moves within 1, 2 or 3 Standard Deviations, as the body of the Platykurtic midsection is wider than a normal distribution.
– Wider midsection = higher probability or more frequency of intermediate moves compared to a normal distribution.
– Negative Kurtosis suggests OTM Calls & OTM Puts and ITM Calls & ITM Puts are overpriced.
Specifically, with Kurtosis, you will get differing views on how useful it is for retail trading, especially from ex-market makers/floor traders.  Namely, because with liquid products, options are never mispriced.  The price of the an option is what you are able to buy it marginally below Theoretical Price; or, sell it marginally above the Theoretical Price for that day. Though, you will get consensus with the value of using Skew for retail trading purposes. So, if you use a paid service that provides IV data, make sure at minimum the service provides measures of Skewness, as part of the package.  If it provides Kurtosis (without additional charges), it's a bonus and a clear differentiator.  
Ranges and extremes of Implied Volatility, Skewness and Kurtosis act as magnetic fields pushing/pulling price towards/away from its mean/mode, as measurable dimensions of price.

Conclusion: It is the Demand/Supply of Put/Calls, priced by Implied Volatility that shapes the Skew (and Kurtosis) of the underlying traded. In turn, forming the Probability traits of how price occurrences are to be distributed from where the live price is trading. Always choose a higher probability and lower reward trade to control the risks.  Want more on factoring the increase/decrease in forecasted IV to Theoretically Price an option or spread?