Bài giảng Tài chính phái sinh: Chương 15 - Các ký tự Hy lạp

Options, Futures, and Other Derivatives, 6
th
Edition, Copyright © John C. Hull 2005
15.1
Các ký tự Hy lạp
Chương 15
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.2
Ví dụ

Μ τ νγν η◊νγ  β〈ν µ τ θυψ ν χη ν µυα κι υ ộ đ ộ ề ọ ể
Χηυ ℜυ τρ γι〈 ∃300,000 τρν 100,000 χ πηι υ ị ổ ế
κηνγ τρ χ τ χả ổ ứ

S
0
= 49, K = 50, r = 5%, σ = 20%,
T = 20 τυ ν, ầ µ = 13%

Γι〈 τρ τηεο Βλαχκ−Σχηολεσ χ α χ πηι υ λ◊ ị ủ ổ ế
∃240,000

Νγν η◊νγ σ πη∫νγ νγ α ρ ι ρο χηο µνη β νγ χ〈χη ẽ ừ ủ ằ
ν◊ο γι χ λ ι νηυ ν ∃60,000?để ữ đượ ợ ậ
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.3
Vị thế Naked & Covered
ς τη Νακεδ ị ế

(τηαµ για τη τρ νγ νη νγ κηνγ χ⌠ τ◊ι σ ν χ σ ị ườ ư ả ơ ở
τρονγ ταψ − Ν∆)
Κηνγ λ◊µ γ χả
ς τη Χοϖερεδ
(τηαµ για τη τρ  νγ χ⌠ τ◊ι σ ν χ σ τρονγ
ταψ −Ν∆)
Μυα 100,000 χ πηι υ ηµ ναψổ ế
Χ ηαι χηι ν λ χ τρν υ γψ χηο νγν ả ế ượ đề
η◊νγ νη νγ ρ ι ρο 〈νγ κữ ủ đ ể
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.4
Chiến lược chấm dứt lỗ
Χηι ν λ  χ ν◊ψ λιν θυαν   ν:

Μυα 100,000 χ πη ν νγαψ κηι γι〈 τ ổ ầ đạ
  ν ∃50

Β〈ν 100,000 χ πη ν νγαψ κηι γι〈 γι µ
ξυ νγ δ ι ∃50ố ướ
Χηι ν λ χ πη∫νγ νγ α ρ ι ρο τ νγ ế ượ ừ ủ ưở
χη νγ ν γι ν ν◊ψ τη χ σ κηνγ µανγ ừ đơ ả ự ự
λ ι ηι υ θυ χαο.ạ ệ ả
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.5
Delta (Xem Hình 15.2, trang 345)

∆ελτα (∆) λ◊ τ λ τηαψ ι γι〈 θυψ ν ỷ ệ đổ ề
χη ν σο ϖ ι γι〈 χ α σ ν πη µ χ σọ ớ ủ ả ẩ ơ ở

Giá quyền chọn
A
B
Độ dốc = ∆
Giá cổ phiếu
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.6
Phòng ngừa Delta

ι υ ν◊ψ λιν θυαν ν ϖι χ δυψ τρ µ τ Đ ề đế ệ ộ
δανη µ χ τρυνγ λ π ϖ ι δελταụ ậ ớ

∆ελτα χ α µ τ θυψ ν χη ν µυα κι υ Χηυ
ℜυ ι ϖ ι µ τ χ πηι υ χ⌠ συ τ σινη λ ι đố ớ ộ ổ ế ấ ợ
χ τ χ ổ ứ q λ◊

N (d
1
)e
– qT

∆ελτα θυψ ν χη ν β〈ν κι υ Χηυ ℜυ λ◊
e
– qT
[N (d
1
) – 1]
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005

15.7
Phòng ngừa Delta
(tiếp theo)

Πη ι τη νγ ξυψν χν ι λ ι ϖ τη πη∫νγ ả ườ đố ạ ị ế
νγ α

Πη∫νγ νγ α ∆ελτα λ◊ µ τ λ α χη ν      χ
ϖι τ ρα νη µ τ θυψ τ χ γιαο δ χη µυα χαο, “ế ư ộ ắ ị
β〈ν τη π”ấ

Ξεµ Β νγ 15.2 (τρανγ 350) ϖ◊ 15.3 (τρανγ 351) ϖ
νη νγ ϖ δ ϖ πη∫νγ νγ α δελτα
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.8
Sử dụng hợp đồng giao sau để
phòng ngừa Delta

∆ελτα χ α µ τ η π νγ γιαο σαυ λ◊ ủ ộ ợ đồ e
(r-q)T
νην
ϖ ι δελτα χ α η π   νγ γιαο νγαψ

∆ο ϖ ψ ϖ τη χ ν χ⌠ χ α πη∫νγ νγ α δελτα
τρονγ η π   νγ γιαο σαυ λ◊ e
-(r-q)T
νην ϖ ι ϖ
τη χ ν χ⌠ τρονγ η π   νγ γιαο νγαψ τ  νγ  νγ
Options, Futures, and Other Derivatives, 6th Edition,

Copyright © John C. Hull 2005
15.9
Theta

Τηετα (Θ) χ α µ τ σ ν πη µ πη〈ι σινη (ηο χ ủ ộ ả ẩ ặ
µ τ δανη µ χ πη〈ι σινη) λ◊ τ λ τηαψ   ι γι〈
τρ σ ν πη µ  ⌠ σο ϖ ι τηαψ   ι χ α τη ι
γιαν σ η υ.

Τηετα χ α µ τ θυψ ν χη ν µυα ηο χ β〈ν
τη νγ λ◊ σ µ. ι υ ⌠ χ⌠ νγη α λ◊ ν υ τη ι ườ ố Đề đ ĩ ế ờ
γιαν τρι  ι, γι〈 τ◊ι σ ν χ σ ϖ◊   βι ν   νγ
χ α ν⌠ ϖ ν κηνγ τηαψ   ι τη γι〈 τρ χ α
θυψ ν χη ν σ γι µề ọ ẽ ả
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.10
Gamma

Γαµµα (Γ) τ λ τηαψ   ι χ α δελτα (∆) σο
ϖ ι τηαψ   ι γι〈 χ α σ ν πη µ πη〈ι σινη

Γαµµα λ◊ λ ν νη τ   ι ϖ ι νη νγ θυψ ν
χη ν γ ν ϖ ι τι ν µ τ (ξεµ Ηνη 15.9, τρανγ
358)
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.11
Gamma nhắm đến Phòng ngừa Delta
Các lỗi do độ cong gây ra

(Hình 15.7, trang 355)

S
C
Giá cổ phiếu
S'
Giá quyền
chọn mua
C''
C'
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.12
Giải thích về Gamma

  ι ϖ ι µ τ δανη µ χ τρυνγ λ π ϖ ι ∆ελτα,
   ∆Π ≈ Θ ∆
τ
+ Γ∆
Σ

2

∆Π
∆S
Gamma âm
∆Π
∆S
Gamma dương
Options, Futures, and Other Derivatives, 6th Edition,

Copyright © John C. Hull 2005
15.13
Mối quan hệ giữa Delta, Gamma,
và Theta
Đối với một danh mục các sản phẩm
phái sinh trên một cổ phiếu có suất lợi
cổ tức liên tục q
Θ ∆ Γ Π+ − + =( )r q S S r
1
2
2 2
σ
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.14
Vega

ςεγα (ν) λ◊ τ λ τηαψ ι γι〈 τρ δανη µ χ ỷ ệ đổ ị ụ
σ ν πη µ πη〈ι σινη σο ϖ ι τηαψ ι χ α ả ẩ ớ đổ ủ độ
βι ν νγế độ

ςεγα χ⌠ ξυ η νγ λ ν νη τ ι ϖ ι νη νγ ướ ớ ấ đố ớ ữ
θυψ ν χη ν γ ν ϖ ι τι ν η ν (Ξεµ ề ọ ầ ớ ề ơ
Ηνη15.11, τρανγ 361)
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.15
Quản lý Delta, Gamma, & Vega
•
∆ χ⌠ τη τηαψ ι β νγ χ〈χη τηαµ για τη ể đổ ằ ị

τρ νγ τ◊ι σ ν χ σườ ả ơ ở

ι υ χη νη Để đ ề ỉ Γ & ν χ ν πη ι τηαµ για τη
τρ  νγ θυψ ν χη ν ηο χ σ ν πη µ πη〈ι ề ọ ặ ả ẩ
σινη κη〈χ
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.16
Rho

Ρηο λ◊ τ λ τηαψ   ι γι〈 τρ σ ν
πη µ πη〈ι σινη σο ϖ ι τηαψ   ι λι
συ τ

ι ϖ ι θυψ ν χη ν τι ν τ , χ⌠ 2 λο ι Đố ớ ề ọ ề ệ ạ
ρηοσ
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.17
Phòng ngừa rủi ro trong thực tế

Χ〈χ νη◊ γιαο δ χη τη  νγ   µ β ο ρ νγ δανη
µ χ χ α η τρονγ µ τ νγ◊ψ χ⌠ τ νη τ µ τ λ ν
τρυνγ λ π ϖ ι δελτα. ậ ớ

Β τ χ κηι ν◊ο χ⌠ χ η ι λ◊ η χ ι τηι ν ấ ứ ơ ộ ọ ả ệ
γαµµα ϖ◊ ϖεγα

∆ανη µ χ χ◊νγ λ ν τη πη∫νγ νγ α ρ ι ρο χ◊νγ ụ ớ ừ ủ
τ τ ν κµ.

Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.18
Phân tích tình huống
Πην τχη τνη ηυ νγ λ◊ ϖι χ κι µ   νη τ〈χ
  νγ χ α νη νγ γι   νη κη〈χ νηαυ ϖ γι〈 τ◊ι
σ ν ϖ◊   βι ν   νγ λν γι〈 τρ δανη µ χ
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.19
So sánh phòng ngừa rủi ro với việc
tạo ra một quyền chọn lai tạp

Κηι χηνγ τα πη∫νγ νγ α ρ ι ρο, χηνγ τα τηαµ
για νη νγ ϖ τη β π ữ ị ế đắ ∆, Γ, ν, ϖν ϖν.

Κηι χηνγ τα τ ο ρα µ τ θυψ ν χη ν λαι τ π,
χηνγ τα χη ν νη νγ ϖ τη κ τ η π χ ọ ữ ị ế ế ợ đượ
∆, Γ, & ν.
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.20
Bảo hiểm danh mục

ς◊ο τη〈νγ 10 ν µ 1987, νηι υ νη◊ θυ ν λ ă ề ả
δανη µ χ   χ γ νγ τ ο ρα µ τ θυψ ν χη ν
β〈ν τρν µ τ δανη µ χ λαι τ π

 ι υ ν◊ψ λιν θυαν   ν ϖι χ βαν   υ β〈ν  
δανη µ χ (ηο χ χ〈χ η π νγ γιαο σαυ χη ụ ặ ợ đồ ỉ

σ )   κ τ κ π ∆ χ α θυψ ν χη ν β〈ν
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.21
Bảo hiểm danh mục
(tiếp theo)

Κηι γι〈 τρ χ α δανη µ χ τ νγ, ∆ χ α θυψ ν
χη ν β〈ν τρ νν µ τ η ν ϖ◊ µ τ ϖ◊ι δανη
µ χ βαν υ σ χ µυα λ ι.ụ đầ ẽ đượ ạ

Κηι γι〈 τρ χ α δανη µ χ γι µ, ∆ χ α θυψ ν
χη ν β〈ν τρ νν µ νηι υ η ν ϖ◊ σ δανη µ χ
   χ β〈ν  ι σ νηι υ η ν.
Options, Futures, and Other Derivatives, 6th Edition,
Copyright © John C. Hull 2005
15.22
Bảo hiểm danh mục
(tiếp theo)
Χηι ν λ  χ ν◊ψ   κηνγ µανγ λ ι ηι υ θυ
χαο τρονγ νγ◊ψ 19 τη〈νγ 10 ν µ 1987