ELN Decumulator
ELN Decumulator is a direct subtype of ELN T1
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TYPE INCLUSION RELATIONSHIPS
AVAILABLE FUNCTIONS
AVAILABLE CREATE FUNCTION KEYS
TYPICAL OBJECTS OF TYPE ELN Decumulator
This type represents what is commonly known as "Decumulator Equity Linked Note".
A typical term sheet is the here.
Summary
The note obliges the investor to sell a generally variable number of shares of a given underlying equity accrued in a special nominal account on a periodic basis at an agreed fixed price.
There also exists a knock-out barrier that is observed throughout the note's life with a given frequency.
If the note is knocked out, the investor must buy the accumulated shares and the note expires.
The note can be regarded as the reverse of ELN Accumulator.
Details
Underlying
The note references one stock or a stock index S
At any given observation time t in the future, this stock (or stock index) will have the corresponding market price S(t)
The note also defines a fixed so-called reference price S⁰
The payoff and the various triggers depend only on the performance P(t) - also referred to as growth factor - defined as follows:
P(t) = S(t)/S⁰
From a quantitative perspective, the performance P(t) may be regarded as the note's underlying.
Coupon
This note does not pay a regular interest rate coupon, although the accumulator payment below may be regarded as an equity linked coupon.
Knock-In
This note does not have a knock-in provision
Redemption
This note does not have a redemption provision
Shares Accrual
A certain daily number of shares Nᴰ accrues nominally (but not yet physically from the investor's point of view) on a special account on behalf of the investor on every business day until the note's maturity (included) or the date of a knock-out event (not included), whichever comes first.
If a leverage clause applies represented by a multiplier L (typically 2), on every day t when the performance P(t) falls below a given strike K, LNᴰ additional shares accrue nominally to the special account on that day.
Mathematically, it is easier to represent the number of accrued shares with a negative number and assume the investor will have to buy this negative number of shares, which is equivalent to selling the corresponding positive number of shares.
If a(t) denotes the total (negative) number of shares accrued on the special account by the close of the date t, then on the next business day t+1 it holds:
a(t+1) = a(t) - LNᴰ
provided that t+1 is not a shares settlement day, as described below.
Note, the investor has no ownership of the shares as their number accrues on the special account, but will be obligated to sell them (i.e. buy the accrued negative number of shares) on the specified settlement dates.
Accumulator Payment
As long as no knock-out event has occurred, on specific dates Tᴬᴾ₁ , Tᴬᴾ₂ , ... , Tᴬᴾₚ, the investor should sell to the issuer at a fixed price K the accrued number of shares -a(t) described above, which is equivalent to buying a(t) shares.
The dates Tᴬᴾ₁ , Tᴬᴾ₂ , ... , Tᴬᴾₚ are typically set through the stipulation of a shares settlement frequency, such as biweekly.
On each such stipulated date t, the shares transaction is settled with one or two business delay at t' = t+1 or t+2
This shares transaction has a value to the investor that is equivalent to the following cash payoff as of time t'
a(t) ( S(t') - K S⁰ )
since for each share the investor realizes a profit of S(t') - K S⁰
Note, the current implementation uses the formula a(t) ( S(t) - K S⁰ ), which is equivalent as long as there exists no ex-dividend date between t and t'
Also note the accrual account is reset to 0 immediately after settlement.
Knock-Out
A knock-out event may occur at any time t that is part of a predefined set of u knock-out observation dates Tᴷᴼ₁ , Tᴷᴼ₂ , ... , Tᴷᴼᵤ.
The dates Tᴷᴼ₁ , Tᴷᴼ₂ , ... , Tᴷᴼᵤ are typically set through the stipulation of a knock-out observation frequency, such as monthly.
The knock-out event depends on the performance P(t) and occurs if:
P(t) ≥ BKO
where BKO is a fixed number - such as 105% - referred to as the knock-out barrier.
In general, if a knock-out event occurs, the note terminates and the investor must purchase the accumulated shares at the fixed strike price K
Often a guarantee exists that affects the payoff from a knock-out event.
Assuming the knock-out event occurs on a date T, the applicable total accrued number of shares will be as of the close of the previous business day, i.e. equal to a(T-1)
If we denote by a the applicable accrued number of shares (negative number), the following 4 cases apply.
No guarantee
The investor must sell the -a shares (equivalent to buying a shares) at the delayed settlement date T' = T+1 or T+2, depending on the agreed settlement delay.
The equivalent cash payoff on T' will be a ( S(T') - K S⁰ )
Example
a = -40 shares, S(T') = 103 USD, K = 110%, S⁰ = 100 USD
Then payoff = -40 (103 USD - 110% 100 USD) = -40 (103 USD - 110 USD) = -40 (-7 USD) = 280 USD
Guaranteed initial period with settlement immediately after the KO
Like above, the note expires at KO, but the a shares are replaced with -(Dᴳ - d)Nᴰ + a, where:
Dᴳ = number of business days in the guaranteed period
d = total number of business days on which shares have been accrued since inception until KO
In effect, the investor must sell the -a shares (equivalent to buying a shares) plus those extra shares that would have been accumulated from KO until the end of the guaranteed period under the assumption of L = 1
Example with same parameters as above
Dᴳ = 22 days, d = 10 days, Nᴰ = 20 shares per day
Then payoff = (-(22 - 10) 20 + -40) (103 USD - 110% 100 USD) = (-12 * 20 - 40) (-7 USD) = -280 (-7 USD) = 1960 USD
Guaranteed initial period with settlement immediately after the end of the guaranteed period
The note stays alive until the end of the guaranteed period with shares being accrued as if the KO had not happened.
Then at the end of the guaranteed period the note expires and the investor must sell the accrued shares, if any.
If the end of the guaranteed period is Tᴳ, the final shares transaction will occur at the delayed settlement date Tᴳ' = Tᴳ+1 or Tᴳ+2, depending on the agreed settlement delay.
The equivalent cash payoff on Tᴳ' will be aᴳ ( S(Tᴳ') - K S⁰ ), where:
aᴳ = number of shares (negative number) actually accrued in the special account until (including) Tᴳ
Example with same parameters as above
aᴳ = -620 shares
Then payoff = -620 (103 USD - 110% 100 USD) = -620 (-7 USD) = 4340 USD
Guaranteed minimum number of shares
The note expires at KO, but the a shares are replaced with -Nᴳ - aₛ, where:
Nᴳ = minimum guaranteed total number of shares (positive number) that the investor must sell throughout the life of the note
aₛ = total number of shares (negative number) that have been settled since inception until KO
Example with same parameters as above
Nᴳ = 440 shares
aₛ = -240 shares
Then payoff = (-440 - -240) (103 USD - 110% 100 USD) = -200 (-7 USD) = 1400 USD