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All that is described in the last topic https://smart-lab.ru/blog/572400.php refers to the price of the option. It has been calculated in advance, the volatility and you know how many times for 100 bought for 99 sold. In General, this is the price of the option. Despite the fact that no matter where will price.
the same thing happens with our household. Let me remind you how we felt SKO https://smart-lab.ru/blog/572106.php .(The CummaN X^2-SREDNEE^2)/N-1. As can be seen, the movement of prices in the calculation of volatility does not participate. If we average was 0.01 and the price changed to 0.01 uniformly and rectilinearly, it is 0. And if the price has gone and went, and you will not buy and will not buy, according to the Delta change option will be equal to the change of your position in BA. But the option is still hardwired IV in tette, which will be to reduce the price. However, the primary tool we have BA and the price is formed from his movements. An option is a derivative instrument. And if we did what is not lost on DH, why must deduct money from the cost of the option? And it is necessary. Need to write off tattoo. Well, we tattoo written off and attributed to IV. And that is the game the market maker. Now, if you'll be able to sell the option on a new IV + expectation that things go well, we are in the black.
we Have one option to expire and we need him tattoo blamed on anyone. We are interested in the return movement. Rather movements within our Delta. We are going to earn.
we Have a 100000 asset and we value the Delta purchase. If we have ox 30%, it means per day 30/256^0.5=1.875%. We leveled the Delta every 0.01 change. BA has to go to 0.01/range(0,000039)=257. Or 0.25% of the BA. Well, we 0.01 Delta acquiring 2.57 points. Price turned, sold of 2.57. How many times? If the day of the ox we 1.875 percent, it is not difficult to find and the dispersion from which it was built. 0,01875^2=0.00035. And our change in BA per Delta of 0.0025^2. Divide one by the other we get 56 steps. What would earn/lose, we need two steps (bought/sold), 52/2(-1 return)=25 times by 2.57 points. Get 65 points.
Now, if we increase the step. We have increased the pitch/range, increasing the price of the idle step. And we get the same thing, but minus (the change in Delta/gamma*change of the Delta) Or the change in the Delta squared / range.
could be easier. With all the transfers from one year to the day. (S^2*sig^2/256 days in a year/2) and all this is multiplied by gamma. If someone does not guessed, then I got theta. And now. Our step Delta squared/scale we need to subtract from it. Will theta Delta hedge with your step.
So what is the step better? And you to buy or sell? In General, this is a philosophical question. Now if the option we have quarterly with tettey $ 50, rare DX with an error of 0.01 in 5 roubles sensitive. If weekly, then the same step of 0.01 will give an error of 1 rubel at tette 200. But the number of transactions is 20 times more and at a fee you can not notice the benefit. Here you choose.
will Focus on the other. As you have noticed we now have two tatty. One option theta and this is minus 0.5*Gamma*S^2*sigIV^2/256 (for purchase) and theta DH of 0.5*Gamma*S^2*sigRV^2/256 and that's a plus. From one another is taken away. As gamma and S we are equal, we come to (sigIV^2-sigRV^2)*(0.5*gamma*S^2)/256 for the day. The second member where the Gamma of the option we bought, get our foot on which we HH. And we get this effect. With the growth of RV on IV 10% will receive 100 points, and in the fall, RV IV less than 10% will lose 72 points. Arbitration occurs a hole that is quickly eliminated. And we have the risk gepov. And do you even know where to stick it. That would be justice. But this place we will discuss another time.
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