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