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Option Deltas and Probabilities

In the course of writing about options, I have generally focused on market phenomena and ideas with few articles that are more basic or educational in nature.  Since I am currently in the process of writing educational books, I feel it is important that I mention some of the basic tenets of options here on the blog.

The sensitivities of option prices are considered the “Greeks”.  The greeks tell the option trader how sensitive the option price is to changes in underlying market factors.  These market factors involve the movements in the underlying stocks (Delta, Gamma), the movement in implied volatility (Vega), the movement in interest rates (Rho), the passage of time (Theta).  For now I want to focus on the simplest and possibly most important option greek – Delta.

Delta is quite simply the change in the option price given a change in the underlying price.  In the case of stocks, delta’s are generally reported in dollar terms per option contract.  A delta of 1 means that the option will increase in value $1 for every $1 that the underlying increases in price.  A delta of .5 means that the option will increase in value $.50 for ever $1 that the underlying increases in price.  Obviously a negative delta means that you will lose money on the option for every dollar increase in the underlying, so you are effectively short the stock through a long put or short call option position.

The absolute value of the delta on a put option plus the absolute value of the delta on a call option that have the same maturity and same strike price approximately equals 1.  This means that if the delta of the call option is .6 then you can assume that the put option with same strike and same expiration is approximately -.4

The further in the money the call or put options are, the closer their delta’s get to +1 or -1 respectively.  Likewise, the further out of the money the call or put options are, the closer their delta’s get to 0.  By default, if a put option has a delta near zero, then its corresponding call option with same strike and expiration must have a delta close to 1.  If you are exactly in the middle, meaning that your strike is equal to the underlying stock price, then you can expect that your delta would be +.5 for calls and -.5 for puts.

Now comes the fun part.

If we believe that stock prices are normally distributed and follow random brownian motion, that the underlying option prices are correct then the delta’s also can be interpreted as the approximate probability that the option will expire in the money. E.G.  – If you sell an out of the money put option that has a delta of -.27, you can interpret that to mean that the option price suggests that there is a 27% chance that the stock will trade below the strike at the option’s expiration.  This proxy works best for short-term options and does not tell you the probability of how often the stock will touch the strike price between now and expiration, but merely the probability that it expires in the money.

Real Example:

Assume Microsoft is currently trading at $25 and you write 1 August 2011 exchange  traded call contract (100 shares/options) with a strike price of $27 for $.15 per option.  This means that at expiration you will pay $100 per point that MSFT stock exceeds $27 on the August expiration date.  In exchange for selling the upside on MSFT above $27, you received $.15 x 100 = $15 in premium.  The delta of this call option is .15, meaning you will lose .15*100 = $15 per point that microsoft increase in price.  The delta also implies that there is approximately a 15% probability that call option will expire in the money.


Option Spread Strategies: Trading Up, Down, and Sideways Markets (Bloomberg Financial)

  • ISBN13: 9781576602607
  • Condition: New
  • Notes: BRAND NEW FROM PUBLISHER! 100% Satisfaction Guarantee. Tracking provided on most orders. Buy with Confidence! Millions of books sold!

Spread trading—trading complex, multi-leg structures–is the new frontier for the individual options trader. This book covers spread strategies, both of the limited-risk and unlimited-risk varieties, and how and when to use them.

All eight of the multi-leg strategies are here: the covered-write, verticals, collars and reverse-collars, straddles and strangles, butterflies, calendar spreads, ratio spreads, and backspreads. Vocabulary, exercises and quizzes are included throughout the book to reinforce lessons.

Saliba, Corona, and Johnson are the authors of Option Strategies for Directionless Markets.

Posted in Derivatives, Educational, Markets.

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