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Relationship between delta and vega

Discussion in 'Options' started by Samer11, Jan 22, 2016.

  1. Samer11

    Samer11 Active Member


    Lately, I have been playing with option strategies that have positive theta, positive delta and positive vega. The positive theta ensures that the strategy makes money as time passes by. However, the interesting question is how to balance delta and vega.

    As the underlying rises, vol comes down. Hence, the profit of the up-movement of the underlying should compensate for the loss resulting from long vega of the option strategy.

    Now, my quesiton is what is the optimal relationship between delta and vega. For example, if my delta is 100, how big should vega be to equalize profit and loss?

    I am familiar with weighted vega... So if anyone has an idea how to balance vega and delta, please share! Thanks!!
  2. ACS

    ACS Well-Known Member

    What is the structure of your strategy? Positive Theta and Vega sounds like there is a time spread in there which may not be Positive Vega outside of the fantasy world of option analysis software.
  3. GreenZone

    GreenZone Well-Known Member

    It would be useful to see the risk graph and trade orders for the trade you're referring to.

    There is no simple answer to your question.

    A "best" (generic) option strategy doesn't exist.
    The "best" option strategy is based on your opinion on what will happen in the near future with price, volatility, skew....and if you're using multiple expirations, then you'll need to understand term structure and weighted vega as well.

    You can have a structure which does incredibly well with a big and strong move up, where IV gets killed, and skew term structure morph in your favor.
    Having this exact same structure for a market which just goes sideways or falls may then be the worst type of structure to put on.
  4. Samer11

    Samer11 Active Member

    This is an example for an option strategy that is positive theta, positive vega and positive delta.

    The question is how to balance this out.

    Attached Files:

  5. AKJ

    AKJ Well-Known Member

    Hi Samer,

    A regular time spread has positive theta and positive vega, and you can position the strikes such that it also has positive delta (alternatively, you can position he strikes so it is negative delta).

    The challenge with a regular time spread is that it is also negative gamma, meaning as the market moves, you begin to build larger and larger exposure to the market if it continues to move in the same direction. In fast markets, these can be difficult positions to manage.

    I'm not exactly sure how you've constructed the position you show in the attachment, but it looks like some combination of a calendar spread and long straddle/strangle. You have created a very Long Gamma trade which has a relatively narrow band where it is positive theta. On the whole, I wouldn't necessary consider your example a positive theta trade. The trade is likely to turn negative theta at some point during the trade, and when you remain in the narrow band where it is positive theta, it appears to be only slightly positive.

    In general, I see trade construction as picking your poison amongst the greeks. In the example of a calendar spread, in exchange for positive theta, you have to take on negative gamma. The trade succeeds in range-bound, mean-reverting markets, but may lose in strong trending markets. The skill in options trading, which we are all aspiring to master, is to identify markets where certain risk factors are trading for relatively cheap/rich against a range of expected future outcomes, and entering a trade that captures that mispricing.
  6. Samer11

    Samer11 Active Member


    With respect to the strategy that I posted, let me explain the three scenarios:

    1. The underlying goes to the left (it falls): volatility increases, so the whole structure goes up, generating profits because of posivite Vega

    2. The underlying moves sideways. Theta fully kicks in. If vol doesn't crash, the structure is likely to make money

    3. The underlying goes up: the structure sinks due to falling volatility and positive Vega. However, the structure is positive delta, meaning profits will be generated , hopefully big enough to compensate for the falling vol

    So it all comes down to the question that I posted at the beginning: what is the optimal relationship between delta and Vega.

  7. AKJ

    AKJ Well-Known Member

    Hi Samer,

    I can understand and appreciate the desire to find a rule set that will maximize the returns on your trade, but my personal experience is that its just not that simple.

    I don't have a direct answer to your question, but I've analyzed the relationship between VIX/SPX and RVX/RUT in the past, and run regressions to see the nature of their relationship. This is one way to try to determine the optimal relationship between your Delta and Vega. One pitfall of this is that the relationship tends not to be linear, so be careful.

    I would recommend backtesting your trade through different market environments to see how the trade reacts. This is the best way to come up with a rule-set.
    Samer11 likes this.
  8. GreenZone

    GreenZone Well-Known Member

    The risk graph you've shown is known as a "victory spread", which I first saw by the guy that teaches the Tradingology course.
    The risk graph looks like it can't lose no matter what happens.....but that's not the case.
    When you trade options in a single expiration, the expiration line will stay where it is, whereas the T+0 will move up and down.
    When you trade multiple expirations (diagonals, calendars, etc), then the expiration line itself is free to move up and down, which tends to surprise people.

    Hare are my notes:
    Venkat and Samer11 like this.
  9. status1

    status1 Well-Known Member

    I agree with Ron the calendars are a different animal They behave differently than a normal spread That's why I don't trade them It's hard for me to predict which way they will go under different scenarios unless you keep a close eye on them I have an apple trade calendar in my paper trade account just to see how it behaves

    After it went down to the breakeven I placed another calendar to lift up the tent and than again as it kept going down so I was up to 3 calendars that are spread out and while I am under the third tent as it started going back up the first calendar expiration line dipped down and very close to touching the t+0 line So the entire expiration line is moving down the higher the price goes actually more due to the volatility than the price

    I also wanted to mention that since your trade is simulated you may not get the actual fill prices that you see in your paper trade account It may look good on paper but when you get filled the picture will not look the same and even if it does the $47 it's showing at expiration it's not worth it after you factor in the commission and that is only if the price does not change Since SPY has been moving up and I am only guessing that it will continue to move up the calendar expiration will move down and probably end up with a small loss Also with only 5 trading days left you may have to keep an eye on it all day and perhaps try to adjust your way up

    So even if you find the perfect delta vega relationship it will not work well for calendars Each calendar trade is different so having one delt vega relationship to cover all calendars I don't think it's possible
    GreenZone and Samer11 like this.
  10. Samer11

    Samer11 Active Member

    Thanks for your comments!

    I will continue to research this particular option strategy. I believe it makes sense especially during the weeks before earnings releases. You simply open such an option position and close it right before earnings announcement.

    I also believe it makes sense in cases where front-month IV is higher than back-month IV.

    It is certainly complex. However, complexity is just a challenge, it can lead to greater profitability...
    GreenZone likes this.
  11. Samer11

    Samer11 Active Member

    Update #1.
    The strategy generated a nice loss of -145 USD. The IV's of the back-month options went down a little bit. Obviously, the strategy generates a loss if the underlying rallies.

    Appreciate feedback if this stuff still interests you... ;-)

    Attached Files:

  12. Avi

    Avi Member

    There is a direct relation between delta and vega through second derivative. Check out the site and has a good pictorial graph on Vamma and Vanna called second order greeks. Practical application is a trial and an error.

    Venkat likes this.
  13. Samer11

    Samer11 Active Member

    Just a short final update.
    Blow Up!
    The strategy failed. The underlying went up too much and vol fell.

    Attached Files:

    GreenZone likes this.
  14. GreenZone

    GreenZone Well-Known Member

    Thanks for sharing, Samer.
    We tend to learn more from the trades which fail, than the ones which succeed.
    Joe A and Samer11 like this.

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