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# Strategy valuation

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

1. ### Cren1

Hi all

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

--- 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 (&#8776;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!

2. ### Cren1

I'm so sorry for having doubled the post, I ask the moderator to delete this thread because it's a copy of another one. Thank you.

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