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4.1.1. "Bull" structured kollar on the basis of exchange options for the future of the Russian Open Society "United Power Systems" traded in market FORTS



Let's consider an example of construction of strategy on the basis of data of trade FORTS for April, 1st, 2005 All numerical significances, except dates and percent, are expressed in roubles.
Bank basic data:
1. At the moment in market FORTS koll and put one term ekspiratsii on the future of the Russian Open Society "United Power Systems" exchange options bargain with 12 strikes which can coincide;
2. The specification of strikes of exchange options koll and put for April, 1st, 2005 is that:
Strikes 6 exchange options koll on the future of the share of the Russian Open Society "United Power Systems":
SC = (7500, 8000, 8500, 9000, 9500, 10000),
Strikes 6 exchange options put on the future for Russian Open Society "United Power Systems" shares:
SP = (6000, 6500, 7000, 7500, 8000, 8500).
3. Quoted sizes of awards of options koll and put on the future of shares of the Russian Open Society "United Power Systems" as of April, 1st, 2005 are that:
P = (872, 520, 310, 155, 85, 50); Q = (12, 26, 77, 168, 326, 578).
With allowance for BID-ASK cпрэда they are presented to tab. 4.1. (For kollov) and 4.2. (For putov) [47]:
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Table 4.1. The average price of options koll on Russian Open Society "United Power Systems" futures in market FORTS in roubles for April, 1st, 2005
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Table 4.2. The average price of options put on Russian Open Society "United Power Systems" futures in market FORTS in roubles for April, 1st, 2005
4. The present value of the future for Russian Open Society "United Power Systems" shares makes:
Mnow =8204 rbl.
5. To supply liquidity at drawing up of the given optional strategy, the trader of bank can purchase or sell no more E = 10 options with one strike.
6. The trader of bank can make optional strategy of data 6 exchange kollov and 6 exchange putov. In a general view (with unknown persons while quantities of options) she can be written down as follows:
F (P, Q, X, Y, M) = X1 • (-(784,8 or 959,2) + max (M? 7500; 0)) + X2 • (-(468 or 572) + max (M? 8000; 0)) + X3 • (-(279 or 341) + max (M? 8500; 0)) + X4 • (-(139,5 or 170,5) + max (M? 9000; 0)) + X5 • (-(76,5 or 93,5) + max (M? 9500; 0)) + X6 • ((45 or 55) + max (M? 10000; 0)) + Y1 • (-(10,8 or 13,2) + max (6000? M; 0)) + Y2 • (-(23,4 or 28,6) + max (6500? M; 0)) + Y3 • (-(69,3 or 84,7) + max (7000? M; 0)) + Y4 • (-(151,2 or 184,8) + max (7500? M; 0)) + Y5 • (-(293,4 or 358,6) + max (8000? M; 0)) + Y6 • (-(520,2 or 635,8) + max (8500? M; 0)).
The size of the optional award is stipulated by operation type (purchase or sale of the optional contract) and factor BID-ASK of the spread depending on type of operation.
Basic data of the client:
To receive a necessary product, the investor addresses to bank to the serving broker and states following wishes:
1. The investor expects growth of the future for Russian Open Society "United Power Systems" shares c price Mnow = 8204 rbl.
to price ME = 9500 rbl. for date ekspiratsii on June, 9th, 2005 At this expected price level 9500 rbl. the investor wishes to receive the maximum monetary payment. The maximum monetary payment should accept significances big zero;
2. Level of the maximum losses should be limited by size 10000 rbl. [48];
3. The investment product which the client wishes to receive, should have negative cost;
4. To cash 1000 rbl. [49] cразу as a result of acquisition of the given product.
Optimisation problem:
The broker transmits the conditions presented by the client, to the trader on options. Definition of an optimal vector of shares of options (X, Y) answering to the conditions delivered by the client, and the further purchase or sale of the necessary quantity of optional contracts with allowance for BID-ASK a spread will be the basic technical problems of the trader of bank. From the mathematical point of view the finding of optimum shares - is a problem of linear optimisation, differently linear programming, in dimension 12 (as 12 types of options are involved in designed strategy). Target funktsional and restrictions, such as linear inequalities, are described in item 3.1. Also are concretised more low. Methods of linear optimisation are realised in various computing environments, including in widespread software package EXCEL in the form of a standard option «decision Search».
By input of conditions and restrictions 1-6 given sections with allowance for the set numerical significances we will indicate a concrete kind of conditions of 3-6 constructions "bull" structured kollara (item 3.1 see.):
For an interval 0-6000: Y1 + … + Y6? 0;
For an interval 6000-6500:? (Y2 + … + Y6)? 0;
For an interval 6500-7000:? (Y3 + … + Y6)? 0;
For an interval 7000-7500:? (Y4 + … + Y6)? 0;
For an interval 7500-8000: X1? (Y5 + Y6)? 0;
For an interval 8000-8500: X1 + X2? Y6? 0;
For an interval 8500-9000: X1 + X2 + X3? 0;
For an interval 9000-9500: X1 + X2 + X3 + X4? 0;
For an interval 9500-10000: X1 + X2 + X3 + X4 + X5? 0;
For an interval 10000 +?: X1 + X2 + X3 + X4 + X5 + X6? 0.
Monetization possibility in the sizes established by the client registers so:
X1 • (784,8 or 959,2) + X2 • (468 or 572) + X3 • (279 or 341) + X4 • (139,5 or 170,5) + X5 • (76,5 or 93,5) + X6 • (45 or 55) + Y1 • (10,8 or 13,2) + Y2 • (23,4 or 28,6) + Y3 • (69,3 or 84,7) + Y4 • (151,2 or 184,8) + Y5 • (293,4 or 358,6) + Y6 • (520,2 or 635,8) =-1000.
For construction "bull" structured kollara, the client satisfying to all inquiries, the trader expects optimum shares (X, Y). He purchases and sells the necessary quantity of options with allowance for a BID-ASK-spread mortgaged in model. Optimum shares kollov and putov are presented to tab. 4.3. And 4.4.

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\"\"Таблица4.3. Optimum shares kollov a product "bull" structured kollar
Таблица4.4. Optimum shares putov a product "bull" structured kollar
Product characteristics will be the following:
1. Total net-award =-1000 rbl., or a monetization (reception of money resources at once) for the sum 1000 rbl.;
2. The "bull" inclination on all interval of possible changes of the price of the basic asset;
3. At an appreciation of the future for shares of the Russian Open Society "United Power Systems" to prognoznoj prices ME = 9500 rbl. the maximum payment is equal:
max F (P, Q, Xoptimal, Yoptimal, ME = 9500) = 12931 rbl. with allowance for monetizations;
4. At falling of the price of the future for papers of the Russian Open Society "United Power Systems" to 7000 rbl. or more low the investor receives restriction of possible losses:
min M F (P, Q, Xoptimal, Yoptimal, M) = F (P, Q, Xoptimal, Yoptimal, 6000) =? 10000 rbl. with allowance for monetizations.
Payments on a product depending on the price of the basic asset are presented on fig. 4.1.:\""Bull" a Fig. 4.1. "Bull" structured kollar on the basis of quotations of exchange options on futures of the Russian Open Societies "United Power Systems" traded on FORTS: final monetary payment on strategy (axis Y) depending on the price of the basic asset at the moment of performance of options (an axis X)

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A source: Pitchugin Igor Sergeevich. STRUCTURIZATION of OPTIONAL PRODUCTS ON THE BASIS OF the METHOD of OPTIMIZATION of FINAL MONETARY PAYMENTS. The dissertation on competition of a scientific degree of a Cand.Econ.Sci. Moscow - 2007. 2007

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