# 程序代写代做代考 algorithm Multi-Asset Equity-Linked Notes

Multi-Asset Equity-Linked Notes

Multi-Asset

Equity-Linked Notes

Definition

• The par value of this 2-year note is D. It has 12 coupon

dates, E1, E2,…..E12, and can be called back, depending

on the values of two assets 𝑆𝑗

1 and 𝑆𝑗

2 where j is a point in

time

• Each coupon period is 2-month long and begins at Bi,

i=1,…,12. Both Bi and Ei are measured in number of

trading days with B1 = 1

• The full coupon amount D * F is paid in the first coupon

period. F is the coupon rate per period.

• The note is called (and the contract ended) if, at E1 or any

other day k before maturity, each asset price 𝑆𝑘

𝑗

, j=1,2, is

greater than or equal to its callable price C 𝑆0

𝑗

, where C

is a given call factor

• For each coupon period x after the first, only a fraction

𝑛𝑥

𝑁𝑥

of the coupon D * F is paid either at the end of the period

or at call date, whichever comes first. 𝑁𝑥 is the number of

business days in the period and 𝑛𝑥 is the number of

business days when the closing prices of both shares 𝑆𝑘

𝑗

,

j=1,2, are greater than or equal to their low-range values

K 𝑆0

𝑗

where K is a given factor

• At call date, the holder receives par value D and the

coupon

𝑛𝑥

𝑁𝑥

* D * F where x is the period the call occurs

• At maturity, if each share price 𝑆𝐸12

𝑗

is greater than K 𝑆0

𝑗

,

the holder receives D. Otherwise, she receives

min{

𝐷

K 𝑆0

1 𝑆𝐸12

1 ,

𝐷

K 𝑆0

2 𝑆𝐸12

2 }

• At maturity, the holder receives also the coupon

𝑛𝐸12

𝑁𝐸12

* D * F

Assignment

• Write an application that accepts the inputs shown below

and estimates the fair value of the note

Note

• To generate the correlated asset paths, use the BS_Cpath

function previously provided in the library

Algorithm

(1) Set Coupon = 𝑒−𝑟𝐸1∆𝑡𝐷𝐹

(2) Set 𝑆𝐸1

∗ = 𝑚𝑖𝑛

𝑆𝐸1

1

𝑆0

1 ,

𝑆𝐸1

2

𝑆0

2

(3) If 𝑆𝐸1

∗ ≥ 𝐶, then set P = 𝑒−𝑟𝐸1∆𝑡𝐷 and go to step 14,

otherwise continue

(4) Set i = 𝐸1 + 1 and x = 2

(5) Set 𝑆𝑖

∗ = 𝑚𝑖𝑛

𝑆𝑖

1

𝑆0

1 ,

𝑆𝑖

2

𝑆0

2

(6) If 𝑆𝑖

∗ ≥ K, then set 𝑛𝑥 = 𝑛𝑥 + 1

(7) If 𝑆𝑖

∗ ≥ C, then set Coupon = Coupon +

𝑒−𝑟𝑖∆𝑡

𝑛𝑥

𝐸𝑥−𝐸𝑥−1

𝐷𝐹 and P = 𝑒−𝑟𝑖∆𝑡𝐷 and go to step 14.

Otherwise, continue.

(8) If i = 𝐸𝑥, then set Coupon = Coupon +

𝑒−𝑟𝐸𝑥∆𝑡

𝑛𝑥

𝐸𝑥−𝐸𝑥−1

𝐷𝐹 and x = x + 1

(9) Set i = i + 1 and repeat steps (5) through (8) until i =

𝐸12. Do not go through these steps if i = 𝐸12.

(10) Set 𝑆𝐸1

∗ = 𝑚𝑖𝑛

𝑆𝐸1

1

𝑆0

1 ,

𝑆𝐸1

2

𝑆0

2

(11) If 𝑆𝐸12

∗ ≥ K, then set 𝑛12 = 𝑛12 + 1

(12) Set Coupon = Coupon + 𝑒−𝑟𝐸12∆𝑡

𝑛12

𝐸12−𝐸11

𝐷𝐹

(13) Set P = 𝑒−𝑟𝐸12∆𝑡𝐷 min

𝑆𝐸12

∗

𝐾

, 1

(14) Price = P + Coupon