Optimal delta hedging with gamma trading

AJJ

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Hi,

Reading all reactions with regard to my previous posting, I think it is best to explain what I mean by working out an example.
To better understand my explanation, you can set up, manage and work out the example yourself at straddleplanner. com. (my site).

Gamma trading example:
Position to set up:
-Trading date: 14-Jun-08
-By 1000 stock XYZ @ USD 8.58
-By 25 puts “strike 8.50 exp:19-Dec-08 trading at Impl.vol of 41%.
-Interest rate 5%

How to enter straddleplannerdotcom:
1.open straddleplanner .com (unfortunately it is not yet “googleable”, thus type in the url)
2.Chose fundname: “XYZ” (click on NEW… and enter XYZ)
3.By 1000 stock XYZ @ USD 8.58 ( click field below XYZ and enter 1000)
4.Set portfolio date to 14 JUN 08 (Click on agenda icon. Portfolio date is the date on which you want to analyse your position. You can change this date the measure the time decay on your portfolio)
5.Enter interest rate 5% (click in box marked interest on add. Click on the date and change it to 19-Dec-08, click on 0.00 and enter 5).
6.Enter strike (click in box marked STRIKES on add. Click on the date and change it to 19-Dec-08, click on the 0.00 under Volatility to enter 41 and click on the 0.00 under Strike to enter 8.50)
7.Enter number of puts (click in column marked long next to 8.50 and enter 25)

You have now entered the entire strategy and can start analysing:

Press on calculate and all values are shown on screen.
-On the left of volatility you will see the call values (Price: 1.14, Delta: 60.54, Gamma: 15.21, Theta:0.31, Rho: 2.09, Vega: 2.37)
-On the right of Strike you will see the put values (Long: 25, Price: 0.86, Delta: -40.72, Gamma: 16.04, Theta: 0.21, Rho:-1.70, Vega: 2.37)
-On the bottom you will see the totals of the position: (Delta: 18, Gamma: 401, Theta: 5, Rho: -42, Vega: 59.)
-Premium: 2161 (Option price*contract size* number of option)
-Value: 10741 (Stock * stock price + Premium) (this number is the amount of USD or GBP or EU you need to invest to set up this particular position.

If you have the same values on your screen than “Congratulations” .

(you might want to save your position now. )

Now what can we do with this?
As you can see, the delta (18 long) of your portfolio is almost completely hedged.
But what will happen when the stock moves down from 8.58 to 8.02?
(click on 8.58 and enter 8.02 and press calculate)
Now you will see that all values will have changed.

I will not mention all values again, but just concern you with the important ones (for this strategy).
First the delta of the position (total delta) is now short 257 and the position value has increased to 10818. You can now re-hedge your postion again by buying 257 stock XYZ @ 8.02. (click on 1000 and enter 1257 and press calculate) You will see that the the total delta is now 0 and your portfolio value is now 12879.
This process now continues as long as the stock price keeps on changing.
If the stock XYZ for example decreases further to 7.60 you can buy an other 196 stock to re-hedge your position and thereby locking in profits.

Important note; in this example I have let the stock price decrease, but the same will happen when the stock price will increase. (in that case you can sell stock to re-hedge).
Also important is to decide upfront when to re-hedge your position. For example whenever your total delta position is long/short 250, 500….

Hope this helps you in getting a better understanding of what gamma trading is about and how a tool like straddleplannerdotcom can help you to manage positions.

Thanks.

If you have any other strategies, you want to analyse or discuss then please let me know.

AJJ
 
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