Skip to content




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.

Be Sociable, Share!

Posted in Derivatives, Educational, Markets.

Tagged with , , , , , .


3 Responses

Stay in touch with the conversation, subscribe to the RSS feed for comments on this post.

  1. Rower32 says

    One thing i’ve never understood is the concept of negative gamma. In what conditions (positions) is a trader short gamma? Some option traders i know often mention if they are positive or negative gamma. My understanding is when you are long option your delta & gamma is positive vice versa. Or you are short straddle you are both negative delta and gamma. Right?

  2. SurlyTrader says

    You are short gamma when you sell options and long gamma when you buy options. The gamma is largest around the strike of the option and largest close to expiration. You can have a delta of zero with a short straddle but have a very large negative gamma. An option trader or option market maker generally likes to be delta neutral at the end of the trading day and keep the negative gamma capped to minimize tail risk. If you delta hedge your option positions then your negative gamma will cause losses that correspond to the following equation: gamma gain/loss = 1/2 * Gamma * (point change)^2.

  3. Rower32 says

    Many thanks it was very helpful, i hope “how to cap negative gamma” and related topics will be future posts.



Some HTML is OK

or, reply to this post via trackback.



Get Adobe Flash player
Copyright © 2009-2013 SurlyTrader DISCLAIMER The commentary on this blog is not meant to be taken as an investment advice. The author is not a registered investment adviser. There is no substitute for your own due diligence. Please be aware that investing is inherently a risky business and if you chose to follow any of the advice on this site, then you are accepting the risks associated with that investment. The Author may have also taken positions in the stocks or investments that are being discussed and the author may change his position at any time without warning.

Yellow Pages for USA and Canada SurlyTrader - Blogged

ypblogs.com