investitsion portfelning asosiy ko’rsatkichlarini baholash

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nnnn 12-ma’ruza. investitsion portfelning asosiy ko’rsatkichlarini baholash reja: yevropa tipidagi opsiyon uchun, diskret holda, to’la bozorning asosiy ko’rsatkichlarini baholash. 2. opsionning muqobil narxi. teorema. (b,s)– to’la bozorda o’z-o’zini moliyalashtiruvchi mukammal strategiyaga va to’lov majburiyati ga mos: 1) muqobil narxni hisoblash formulasi: 2) vaqt oralig’ining k momentidagi muqobil hedjga mos investor mablag’ini hisoblash formulasi: k=1,2,…,n-1. yoki 1. yevropa tipidagi opsiyon uchun, diskret holda, to’la bozorning asosiy ko’rsatkichlarini baholash (18) (19) (20) 3) - mukammal strategiya uchun k momentidagi aksiya hajmi quyidagi tenglama orqali topiladi: ; k=1,2,…,n 4) - mukammal strategiya uchun k momentidagi bank qo’yilmalari (obligasiya) hajmi quyidagi formulalar bilan hisoblanadi: ; k=1,2,…,n yoki ; k=1,2,…,n (21) (22) (23) faraz qilaylik, yevropa turidagi standart opsiyonda majburiyat (to’lov) funksiyasi fn hamma evolutsiyaga, ya’ni s0, s1, … , sn ga bog’liq bo’lmay oxirgi sn ga bog’liq, ya’ni fn=f(sn) bo’lsin. bularga misol qilib yevropa tipidagi standart sotib olish koll opsiyoni yoki standart sotish put …

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uchun bu yerda k0 (30) formuladagi tengsizlikni k ga nisbatan yechish bilan topiladi: (32) (33) endi bu opsion koll uchun olingan natijalardan bevosita opsiyon put uchun ham natijalar olish mumkin, chunki opsiyon put modelini opsiyon koll modeli orqali quyidagicha ifodalash mumkin: bundan bo’ladi. ekanligidan, tenglikka ega bo’lamiz. (34) unknown-0.unknown unknown-1.unknown unknown-2.unknown unknown-3.unknown unknown-4.unknown unknown-5.unknown unknown-6.unknown unknown-7.unknown unknown-8.unknown unknown-9.unknown unknown-10.unknown unknown-11.unknown unknown-12.unknown unknown-13.unknown unknown-14.unknown unknown-15.unknown unknown-16.unknown unknown-17.unknown unknown-18.unknown unknown-19.unknown unknown-20.unknown unknown-21.unknown unknown-22.unknown unknown-23.unknown unknown-24.unknown unknown-25.unknown unknown-26.unknown unknown-27.unknown unknown-28.unknown unknown-29.unknown unknown-30.unknown unknown-31.unknown unknown-32.unknown unknown-33.unknown unknown-34.unknown unknown-35.unknown unknown-36.unknown unknown-37.unknown unknown-38.unknown unknown-39.unknown unknown-40.unknown unknown-41.unknown unknown-42.unknown unknown-43.unknown unknown-44.unknown unknown-45.unknown unknown-46.unknown unknown-47.unknown unknown-48.unknown unknown-49.unknown unknown-50.unknown unknown-51.unknown unknown-52.unknown unknown-53.unknown unknown-54.unknown unknown-55.unknown unknown-56.unknown unknown-57.unknown unknown-58.unknown unknown-59.unknown unknown-60.unknown unknown-61.unknown unknown-62.unknown unknown-63.unknown unknown-64.unknown unknown-65.unknown 0 1 1 * ) 1 ( s s r + = î í ì - = = = 5 / 2 5 / 1 1 a b r ( ) ( ) ( ) ( …

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0 = = k s b a k k 20 5 1 * 3 2 * 150 ) 1 ( ) ( * 0 * * 0 1 1 = = = - + = = b p s kp b p s s ef c ) , ( 0 0 0 n b p = ) , ( 1 1 1 n b p = ( ) ( ) ) ( * ), 1 ( ), 1 ( ) ( 0 * 0 0 * 0 0 0 * 1 a b s p a s f p b s f s - + - + = n ( ) ( ) ) ( * ) 1 ( ) 1 ( 0 0 0 a b s a s f b s f - + - + ( ) ) ( * ) 1 ( 0 0 a b …

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÷ ø ö ç ç è æ d + = n k k k n k k k k n b g b s b x b x n 1 1 1 0 0 * n p 0 = ÷ ÷ ø ö ç ç è æ d k k b s e ( ) 0 1 b f e r b f e n n n n - + = ÷ ÷ ø ö ç ç è æ ( ) å = + - - + + + = n k k k n n eg r ef r x 1 1 0 ) 1 ( 1 ( ) å = + - - + + + ³ n k k k n n eg r ef r x 1 1 ) 1 ( 1 ) , ( k k k n b p = k n ( ) …

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nnnn 12-ma’ruza. investitsion portfelning asosiy ko’rsatkichlarini baholash reja: yevropa tipidagi opsiyon uchun, diskret holda, to’la bozorning asosiy ko’rsatkichlarini baholash. 2. opsionning muqobil narxi. teorema. (b,s)– to’la bozorda o’z-o’zini moliyalashtiruvchi mukammal strategiyaga va to’lov majburiyati ga mos: 1) muqobil narxni hisoblash formulasi: 2) vaqt oralig’ining k momentidagi muqobil hedjga mos investor mablag’ini hisoblash formulasi: k=1,2,…,n-1. yoki 1. yevropa tipidagi opsiyon uchun, diskret holda, to’la bozorning asosiy ko’rsatkichlarini baholash (18) (19) (20) 3) - mukammal strategiya uchun k momentidagi aksiya hajmi quyidagi tenglama orqali topiladi: ; k=1,2,…,n 4) - mukammal strategiya uchun k momentidagi bank qo’yilmalari (obligasiya) hajmi quyidagi formulalar bilan...

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