Strategy valuation

Discussion in 'Options' started by Cren1, Jun 14, 2011.

  1. Cren1


    Hi all.

    It's my first thread in this forum, so please warn me if I'm making any behavioural mistake.

    I'd like to tell you the following options' strategy in order to gather some ideas and critics about it.

    (*) This strategy can be used only on instruments whose volatility behaviour is affected by strongly skewness (i.e. during panic selling the implied and historical volatility reach their maximum, during positive trend the implied and historical volatility is quite low) like equities and equity indexes.

    Strategy requirements:

    1. we calculate an arithmetic average on the last 1,500 ATM Put implied volatility daily observations (I suppose we have an historical dataset);
    2. we calculate the positive and negative semistandard deviation from the mean (technically speaking we say "lower/upper partial moment") of the last 1,500 ATM Put daily implied volatility;
    3. the implied volatility term structure must be as much as possible flat or negatively sloped.


    We check the ATM Put implied volatility. If it's 2 semistandard deviations below the mean, we check the requirements.

    If the requirements are checked, we buy a DOTM strangle at the longest expiry date which market makers allow. We sum up the premiums paid for the strangle and we divide this amount by the number of months between the DOTM strangle expiry date and today.

    For example: suppose we pay $ 18 for the strangle by buying $ 8 DOTM Call and $ 10 DOTM Put; suppose the strangle's expiry date is on March 2012. So we make:

    18 [$] / 9 [months] = 2 [$/month]

    Then we will sell each month a Put whose expiry date is the next month. We will choose the strike price which will allow us to earn on average a $ 2 premium.

    Let's see what could happen in the future:

    - strong positive trend = the strategy is totally self financing, maybe the DOTM Call will appreciate slightly but the Gamma curvature is very weak so it's likely the Theta will consume the strangle's premium. It will earn just if the trend is very strong and the DOTM Call will be ITM at expiry date, but we can earn also if the underlying movement is very fast and we gain Vega if we sell before expiry;

    - weak positive trend = read above, the premiums are lost but we have sold 9 Puts during the previous months and we've financed our long position. Low Vega;

    - no movements = weak positive trend;

    - strong negative trend = panic selling = our DOTM strangle will gain a lot of Vega ("Taleb's effect" or "Black Swan") and we make a lot of money. The short Put will loss, but the gains from the long strangle will cover these losses. We have just won the lottery :D

    - weak negative trend = this is the only case, according to my view, the strategy can loose. In this case the strangle is consumed by Theta and Gamma + Vega is not enough against Theta. We loos the strangle premium and the sold financing Put makes other damages. But... If you do in way to sell OTM Puts each month to cover the strangle's premium, this case is very unlikely. Why? Because of (*). This event is very rare, because, in order to make the sold Put ITM, the underlying movement, according to the past history, should be quite fast. If so, we are in the "strong negative trend" environment, and we win.

    Thank you very much for having read this!
  2. Cren1


    Hi all :)

    It's my first message here. So please tell me if I make any behavioural mistake.

    I'd like to tell you about the following strategy, in order to read your opinion and critics about it.

    --- Step 1: select the underlying

    The first step is to select an underlying whose volatility behaviour is affected by skewness. Take the example of equity and equity index: during panic selling periods the options' historical and implied volatility is usually greater than during positive trend periods. Keep in mind this detail (*).

    --- Step 2: check the requirements

    The second step aims to evaluate if the market conditions are good to enter the trade. So...

    1. Consider the last 1,500 daily observations of ATM Put implied volatility and make an arithmetic average of them;
    2. calculate the negative semistandard deviation (or "lower partial secondary moment") of the last 1,500 daily observations of ATM Put implied volatility according to the mean obtained on 1.;
    3. subtract 1.96 (≈2) negative semistandard deviation from the mean;
    4. if the current ATM Put implied volatility is below the value obtained on 3., go to ne next step;

    --- Step 3: the strategy

    Long position: buy a DOTM strangle whose expiry date is as far as possibile (9 months, for example?). You have to buy the most DOTM possible. Now, assuming for example you have just bought the strangle for $ 18 ($ 8 Call + $ 10 Put), you can start the first one of the short positions.

    Short position: let

    18 [$] / 9 [months to expiry] = 2 [$/months]

    the premium you have to earn each month from now to the expiry date selling Put options. The moneyness of the Put is calculated according to the premium you have to earn each month in order to completely finance your long strangle. So you will sell 9 Put options, each one 1-month time left before expiry, from now on. Rounding to the excess, obviously.

    --- Step 4: scenaro analysis

    Let's see what could happen to our portfolio in the following underlying's scenarios:

    - strong positive trend with high volatility = unless the long DOTM Call will go ITM, the Gamma curvature won't be able to appreciate the Call enough to ignore the Theta effect on the strangle. But if the movement is very fast, you'll get positive Vega which, on DOTM option with long expiry time, is usually stronger than Theta. The short Put will give premium, so the result should be slightly positive;

    - weak positive trend with low volatility = you will cover each month a fraction of the strangle cost by selling Put options, the strangle will expire OTM and your final balance sheet will probably be around zero. No benefits from Vega, just some Delta from the sold Put and slightly negative Gamma from long strangle. Result is zero;

    - no trend = weak positive trend with low volatility = see above;

    - strong negative trend with high volatility = panic selling = you've just won the lottery! You will see your short Put will cause you some losses, but the long DOTM strangle will gain a lot of Vega, which will be greater than Theta's effect. This is the famous "Taleb effect" or "Black Swan". You can stop selling Puts each month and choose the best moment to sell your very very profitable strangle full of Vega. Congratulations.

    - weak negative trend with low volatility = this is the only case you can loose your money. It must happen with low volatility (or it will become "panic selling" and you will win the match). In this case you will see that the Gamma is stronger than Vega and your shorted Put will make you some losses. In the meantime the strangle looses its value. But this case is not so frequent, remember? (*)

    What do you thin about it?

    Thank you for the attention!