Attached files
| file | filename |
|---|---|
| EX-23.B - COUNSEL CONSENT - ALLIANZ LIFE INSURANCE CO OF NORTH AMERICA | counselconsent.htm |
| EX-23.A - CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM - PWC - ALLIANZ LIFE INSURANCE CO OF NORTH AMERICA | auditorconsent.htm |
| S-1/A - INDEX ADVANTAGE INCOME ADV S-1A - ALLIANZ LIFE INSURANCE CO OF NORTH AMERICA | iaiadvs1ajuly2021.htm |
Exhibit 99(a) of the Form S-1 Registration Statement – Daily Adjustment Calculation
We designed the Daily Adjustment to provide an Index Option Value for each Index Option with the Index Precision Strategy, Index Guard Strategy, and Index
Performance Strategy on Business Days other than the Term Start Date or Term End Date. The Daily Adjustment approximates the Index Option Value on the Term End Date, adjusting for:
(i) any Index gains during the Term subject to the Precision Rate, Cap, DPSC, and/or Participation Rate,
(ii) either any Index losses greater than the Buffer or any Index losses down to the Floor, and
(iii) the number of days until the Term End Date.
The Daily Adjustment formula has two primary components: (i) the change in Proxy Value, and (ii) accumulated proxy interest, which are added
together and then multiplied by the Index Option Base. We designed the Daily Adjustment to estimate the present value of positive or negative Performance Credits on the Term End Date. You should note that even if your selected Index(es) experience
positive growth, the Daily Adjustments may be negative because of other market conditions, such as the expected volatility of Index prices and interest rates. The Daily Adjustment for the Index Protection Strategy with Cap and the Index Protection
Strategy with Declared Protection Strategy Credit (DPSC) will never be negative.
DAILY ADJUSTMENT FORMULA
The formula for the calculation of the Daily Adjustment is as follows:
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base
Where:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value)
|
| (b) |
proxy interest = beginning Proxy Value x (1 - time remaining during the Term)
|
CALCULATING CHANGE IN PROXY VALUE
The change in Proxy Value represents the current hypothetical value of the Proxy Investment (current Proxy Value), less the cost of the Proxy Investment on the
Term Start Date (beginning Proxy Value).
The current Proxy Value is the Proxy Value calculated on the same day as the Daily Adjustment. The beginning Proxy Value is the Proxy Value calculated on the Term
Start Date.
The Proxy Value is calculated differently for each Crediting Method.
For the Index Precision Strategy, the Proxy Value involves tracking two hypothetical derivatives and
is calculated using the following formula:
[Precision Rate x (at-the-money binary call)] – (out-of-the-money put)
With respect to our Proxy Value formula, we designed the at-the-money binary call to value the potential for gains equal to the Precision Rate if on the Term End
Date, the Index Value is greater than or equal to the Index Value on the Term Start Date, and the out-of-the-money put to value the potential for Index losses greater than the Buffer for the Index Precision Strategy. It is important to note that the
out-of-the-money put will almost always reduce the Daily Adjustment, even when the current Index price on a Business Day is higher than the Index Value on the Term Start Date. This is because the risk that the Index Value could be lower on the Term End
Date is present to some extent whether or not the current Index price on a Business Day is lower than the Index Value on the Term Start Date.
For the Index Guard Strategy, the Proxy Value involves tracking four hypothetical derivatives and is
calculated using the following formula:
Proxy Value = (at-the-money call) – (out-of-the-money call) – (at-the-money put) + (out-of-the-money put)
With respect to our Proxy Value formula, we designed the at-the-money call and out-of-the-money call to value the potential for Index gains up to the Cap and the
at-the-money put to value the potential for Index losses, but add back the out-of-the-money put to mimic the protection of the Floor for the Index Guard Strategy. It is important to note that the at-the-money put will almost always reduce the Daily
Adjustment, even when the current Index price on a Business Day is higher than the Index Value on the Term Start Date. It is also important to note that the out-of-the-money put will almost always reduce, and never exceed, the negative impact of the
at-the-money put for the Index Guard Strategy.
For the Index Performance Strategy, the Proxy Value involves tracking three hypothetical derivatives
and is calculated using the following formula:
Proxy Value = (at-the-money call) – (out-of-the-money call) – (out-of-the-money put)
With respect to our Proxy Value formula, we designed the at-the-money call and out-of-the-money call to value the potential for Index gains up to the Cap, and the
out-of-the-money put to value the potential for Index losses greater than the Buffer for the Index Performance Strategy. Similar to the Index Precision Strategy, it is important to note that the out-of-the-money put will almost always reduce the Daily
Adjustment, even when the current Index price on a Business Day is higher than the Index Value on the Term Start Date. This is because the risk that the Index Value could be lower on the Term End Date is present to some extent whether or not the
current Index price on a Business Day is lower than the Index Value on the Term Start Date. For purposes of the Proxy Value formula the value of the out‑of‑the‑money call will be zero if an Index Option is
uncapped.
For the Index Protection Strategy with Cap, the Proxy Value involves tracking two hypothetical
derivatives and is calculated using the following formula:
Proxy Value = (at-the-money call) – (out-of-the-money call)
With respect to our Proxy Value formula, we designed the at-the-money call and out-of-the-money call to value the potential for Index gains up to the Cap for the
Index Protection Strategy with Cap.
For the Index Protection Strategy with DPSC, the Proxy Value involves tracking one hypothetical
derivative and is calculated using the following formula:
Proxy Value = DPSC x (at-the-money binary call)
With respect to our Proxy Value formula, we designed the at-the-money binary call to value the potential for gains equal to the DPSC if on the Term End Date, the
Index Value is greater than or equal to the Index Value on the Term Start Date.
DERIVATIVE DESCRIPTIONS
At-the-money binary call (AMBC)
This is an option to buy a position in the Index on the Term End Date at the strike price of one. On a Term End Date the AMBC’s value is equal to one if the
current Index price on a Business Day is greater than or equal to the Index Value on the Term Start Date, or zero otherwise.
At-the-money call (AMC)
This is an option to buy a position in the Index on the Term End Date at the strike price of one. On a Term End Date the AMC’s value is equal to the current Index
price on a Business Day divided by the Index Value on the Term Start Date, then minus one, the difference being no less than zero.
At-the-money put (AMP)
This is an option to sell a position in the Index on the Term End Date at the strike price of one. On a Term End Date the AMP’s value is equal to one minus the
quotient of the Index Value on the Term Start Date divided by the current Index price on a Business Day, the difference being no less than zero.
Out-of-the-money call (OMC)
This is an option to buy a position in the Index on the Term End Date at the strike price of (one plus the Cap). On a Term End Date the OMC’s value is equal to the
current Index price on a Business Day divided by the Index Value on the Term Start Date, then minus the sum of one plus the Cap, the difference being no less than zero. For purposes of the Proxy Value formula if
an Index Option is uncapped the OMC will be zero.
Out-of-the-money-put (OMP)
This is an option to sell a position in the Index on the Term End Date at the strike price of (one either minus the Buffer or plus the Floor, depending on the
Index Option). On a Term End Date the OMP’s value is equal to one either minus the Buffer or plus the Floor, then minus the quotient of the Index Value on the Term Start Date divided by the current Index price on a Business Day, the difference being no
less than zero.
The proxy interest is an amount of interest that is earned to provide compensation for the cost of the Proxy Investment at the Term Start Date. The proxy interest
is approximated by the value of amortizing the cost of the Proxy Investment over the Term to zero. The formula for proxy interest involves the calculation of: (i) the beginning Proxy Value (the formula for which varies depending on the Crediting
Method, as previously discussed), and (ii) the time remaining during the
Term. The time remaining during the Term is equal to the number of days remaining in the Term divided by the Term length. The Term length is 365 days for a 1-year
Term Index Option; 1,095 days for a 3-year Term Index Option; and 2,190 days for a 6-year Term Index Option. The proxy interest may be significantly different from current interest rates available on interest bearing investments.
PROXY VALUE CALCULATION
Throughout the Term, on Business Days other than the Term Start Date or Term End Date, we calculate each hypothetical derivative daily using the Black Scholes
model for valuing a European Option. The purpose of this calculation is to determine the market value of your allocation.
PROXY VALUE INPUTS
Term TD return – The Index price at the end of the current Business Day divided by the Index Value on the Term Start Date.
The Index prices are provided daily by Bloomberg or another market source.
Dividend yield – The annualized dividend yield as approximated by a market source. We use dividend yields consistent with
the market pricing of options. Since dividends typically reduce Index prices, a higher dividend yield will lead to a lower expected Index price.
For the EURO STOXX 50® dividend yield, we adjust the dividend yield for the exchange rate. The iShares® MSCI Emerging Markets ETF does not
use a dividend yield because it has discrete dividends. We instead subtract the present value of expected dividends during the Term from the Index price. The present value of dividends is calculated each day and includes dividends expected to be paid
during the remainder of the Term.
Strike price – This varies for each derivative investment as follows.
| • |
For an AMBC, AMC or AMP the strike price is equal to 1.
|
| • |
For an OMC:
|
|
-
|
For Index Options without a Participation Rate, the strike price is equal to 1 plus the Cap.
|
|
-
|
For Index Options with a Participation Rate, the strike price is equal to 1 plus the Cap divided by the Participation Rate.
|
| • |
For an OMP the strike price is equal to 1 minus the Buffer.
|
If an Index Option is uncapped, we do not use the OMC.
Notional amount – For Index Options with a Participation Rate, the notional amount reflects the increase in the amount of derivative
instruments required within the Proxy Investment due to the Participation Rate. The notional amount varies for each derivative investment as follows:
|
•
|
For an AMC or OMC the notional amount is equal to the Participation Rate
|
|
•
|
For an OMP the notional amount is equal to 1
|
If an Index Option is uncapped, we do not use the OMC.
Interest rate –The interest rate is used to present value the strike price from the next Term End Date to the time of
calculation. We use interest rates consistent with market pricing of options with a maturity equal to the length of time remaining during the Term.
Time remaining – This is equivalent to the portion of time remaining during the Term. It is equal to the number of days in
the Term from the Term End Date to the time of the calculation divided by the Term length. The Term length is 365 days for a 1-year Term Index Option; 1,095 days for a 3‑year Term Index Option; and 2,190 days for a 6-year Term Index Option.
Volatility – The volatility of an Index as approximated daily using observed option prices by a market source. The
volatility is used in determining the likelihood and expected amount that the Index Value will differ from the strike price on the next Index Anniversary. As volatility increases, the value of call and put options generally increase.
EXAMPLE: INDEX PERFORMANCE STRATEGY WITH 1-YEAR TERM USING S&P 500® INDEX
Assume you purchase a Contract and allocate your total initial Purchase Payment of $10,000 to the Index Option for the Index Performance Strategy with 1-year Term
using S&P 500® Index. On the Term Start Date the Index Option Base is $10,000, the Cap is 12%, the Buffer is 10% and the Index Value is 1,000. Assume that all Proxy Value inputs except the Index price stay constant throughout the Term. Please note that these examples may differ from your actual results due to rounding.
Term Start Date
On the Term Start Date we calculate the beginning Proxy Value as follows.
|
Strike price
|
AMC = 1
|
OMC = 1.12
|
OMP = 0.90
|
|
Index Value
|
1,000
|
||
|
Term TD return
|
NA
|
||
|
Interest rate
|
0.50%
|
||
|
Dividend yield
|
2.20%
|
||
|
Time remaining
|
1
|
||
|
Volatility
|
15.00%
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 5.10%
|
OMC = 1.66%
|
OMP = 2.41%
|
Beginning Proxy Value = AMC – OMC – OMP = 5.10% – 1.66% – 2.41% = 1.03%
|
Month
|
Index Value
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
Term Start Date
|
1,000
|
5.10%
|
1.66%
|
2.41%
|
1.03%
|
$0.00
|
$10,000.00
|
End of month one
Assume the Index price increased to 1,010 by the end of month one. We calculate the current Proxy Value as follows:
|
Strike price
|
AMC = 1
|
OMC = 1.12
|
OMP = 0.90
|
|
Index price
|
1,010
|
||
|
Term TD return
|
1.00%
|
||
|
Interest rate
|
0.50%
|
||
|
Dividend yield
|
2.20%
|
||
|
Time remaining
|
0.92
|
||
|
Volatility
|
15.00%
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 5.41%
|
OMC = 1.72%
|
OMP = 1.95%
|
Current Proxy Value = AMC – OMC – OMP = 5.41% – 1.72% – 1.95% = 1.74%
In this example the Index price increased since the Term Start Date, which generally increases the Proxy Value. We calculate the Daily Adjustment and Index Option
Value as follows.
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value) = (1.74% - 1.03%) = 0.71%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.03% x (1 - 0.92) =
0.086% |
= [(a) 0.71% + (b) 0.086%] x $10,000 = $79.39
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + $79.39 =
$10,079.39
|
Month
|
Index Price
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
1
|
1,010
|
5.41%
|
1.72%
|
1.95%
|
1.74%
|
$79.39
|
$10,079.39
|
End of month one with changes to Proxy Value inputs
Proxy Value inputs can result in a negative Daily Adjustment even with a positive return in the Index. As in the previous example, assume the
Index price increased to 1,010 by the end of month one. In addition, assume volatility decreased from 15% to 7%, 5%, and 10% for the AMC, OMC and OMP respectively and dividend yield increased from 2.20% to 5%. We calculate the current Proxy Value as
follows:
|
Strike price
|
AMC = 1
|
OMC = 1.12
|
OMP = 0.90
|
|
Index price
|
1,010
|
||
|
Term TD return
|
1.00%
|
||
|
Interest rate
|
0.50%
|
||
|
Dividend yield
|
5.00%
|
||
|
Time remaining
|
0.92
|
||
|
Volatility
|
7.00%
|
5.00%
|
10.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 1.37%
|
OMC = 0.00%
|
OMP = 1.12%
|
Current Proxy Value = AMC – OMC – OMP = 1.37% – 0.00% – 1.12% = 0.25%
In this example the Index price increased since the Term Start Date, which generally increases the Proxy Value. We calculate the Daily Adjustment and Index Option
Value as follows.
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value) = (0.25% - 1.03%) = -0.78%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.03% x (1 - 0.92) = 0.086%
|
= [(a) -0.78% + (b) 0.086%] x $10,000 = -$69.83
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + -$69.83 = $9,930.17
|
Month
|
Index Price
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
1
|
1,010
|
1.37%
|
0.00%
|
1.12%
|
0.25%
|
-$69.83
|
$9,930.17
|
End of month three
Returning to the original assumptions regarding dividend yield (2.20%) and volatility (15.00%), assume the Index price decreased to 950 by the end
of month three. We calculate the current Proxy Value as follows:
|
Strike price
|
AMC = 1
|
OMC = 1.12
|
OMP = 0.90
|
|
Index price
|
950
|
||
|
Term TD return
|
-5.00%
|
||
|
Interest rate
|
0.50%
|
||
|
Dividend yield
|
2.20%
|
||
|
Time remaining
|
0.75
|
||
|
Volatility
|
15.00%
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 2.50%
|
OMC = 0.52%
|
OMP = 3.09%
|
Current Proxy Value = AMC – OMC – OMP = 2.50% – 0.52% – 3.09% = -1.11%
In this example the Index price decreased, which generally decreases the Proxy Value. We calculate the Daily Adjustment and Index Option Value as follows.
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value) = (-1.11% - 1.03%) = -2.14%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.03% x (1 - 0.75) = 0.26%
|
= [(a) -2.14% + (b) 0.26%] x $10,000 = -$187.97
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + -$187.97 = $9,812.03
|
Month
|
Index Price
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
3
|
950
|
2.50%
|
0.52%
|
3.09%
|
-1.11%
|
-$187.97
|
$9,812.03
|
End of month six
Assume the Index price decreased to 910 by the end of month six. We calculate the current Proxy Value as follows:
|
Strike price
|
AMC = 1
|
OMC = 1.12
|
OMP = 0.90
|
|
Index price
|
910
|
||
|
Term TD return
|
-9.00%
|
||
|
Interest rate
|
0.50%
|
||
|
Dividend yield
|
2.20%
|
||
|
Time remaining
|
0.50
|
||
|
Volatility
|
15.00%
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 0.89%
|
OMC = 0.08%
|
OMP = 3.69%
|
Current Proxy Value = AMC – OMC – OMP = 0.89% – 0.08% – 3.69% = -2.88%
In this example the Index price decreased, which generally decreases the Proxy Value. We calculate the Daily Adjustment and Index Option Value as follows.
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value) = (-2.88% - 1.03%) = -3.91%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.03% x (1 - 0.50) = 0.51%
|
= [(a) -3.91% + (b) 0.51%] x $10,000 = -$339.77
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + -$339.77 =
$9,660.23
|
Month
|
Index Price
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
6
|
910
|
0.89%
|
0.08%
|
3.69%
|
-2.88%
|
-$339.77
|
$9,660.23
|
End of month eleven
Assume the Index price increased to 1095 by the end of month eleven. We calculate the current Proxy Value as follows:
|
Strike price
|
AMC = 1
|
OMC = 1.12
|
OMP = 0.90
|
|
Index price
|
1095
|
||
|
Index YTD return
|
9.50%
|
||
|
Interest rate
|
0.50%
|
||
|
Dividend yield
|
2.20%
|
||
|
Time remaining
|
0.08
|
||
|
Volatility
|
15.00%
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 9.37%
|
OMC = 0.87%
|
OMP = 0.00%
|
Current Proxy Value = AMC – OMC – OMP = 9.37% – 0.87% – 0.00% = 8.50%
In this example the Index price increased, which generally increases the Proxy Value. We calculate the Daily Adjustment and Index Option Value as follows.
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value) = (8.50% - 1.03%) = 7.47%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.03% x (1 - 0.08) = 0.94%
|
= [(a) 7.47% + (b) 0.94%] x $10,000 = $841.78
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + $841.78 =
$10,841.78
|
Month
|
Index Price
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
11
|
1,095
|
9.37%
|
0.87%
|
0.00%
|
8.50%
|
$841.78
|
$10,841.78
|
The following table shows for each month during a 1-year Term what the hypothetical Proxy Values, Daily Adjustments, and Index Option Values would
be for different Index prices. Note that all Proxy Value inputs used are the same as in the previous examples. For simplicity we assume the Index Option Base is $10,000 throughout the Term. In reality your Index Option Base changes throughout the Term
with the deduction of any partial withdrawal you request and when we deduct applicable contract fees and charges.
|
Month
|
Index Prices
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
Term Start Date
|
1,000
|
5.10%
|
1.66%
|
2.41%
|
1.03%
|
$0.00
|
$10,000.00
|
|
1
|
1,010
|
5.41%
|
1.72%
|
1.95%
|
1.74%
|
$79.39
|
$10,079.39
|
|
2
|
975
|
3.62%
|
0.94%
|
2.58%
|
0.10%
|
-$75.46
|
$9,924.54
|
|
3
|
950
|
2.50%
|
0.52%
|
3.09%
|
-1.11%
|
-$187.97
|
$9,812.03
|
|
4
|
925
|
1.59%
|
0.25%
|
3.73%
|
-2.39%
|
-$307.94
|
$9,692.06
|
|
5
|
850
|
0.30%
|
0.02%
|
7.54%
|
-7.26%
|
-$785.68
|
$9,214.32
|
|
6
|
910
|
0.89%
|
0.08%
|
3.69%
|
-2.88%
|
-$339.77
|
$9,660.23
|
|
7
|
980
|
2.61%
|
0.33%
|
1.07%
|
1.20%
|
$77.62
|
$10,077.62
|
|
8
|
1,015
|
3.95%
|
0.51%
|
0.36%
|
3.08%
|
$273.31
|
$10,273.31
|
|
9
|
1,100
|
9.95%
|
2.22%
|
0.01%
|
7.72%
|
$745.88
|
$10,745.88
|
|
10
|
1,125
|
12.25%
|
2.83%
|
0.00%
|
9.42%
|
$924.84
|
$10,924.84
|
|
11
|
1,095
|
9.37%
|
0.87%
|
0.00%
|
8.50%
|
$841.78
|
$10,841.78
|
|
Term End Date
|
1,080
|
$10,800.00
|
EXAMPLE: INDEX PERFORMANCE STRATEGY WITH 3-YEAR TERM USING S&P 500® INDEX
This example uses the same assumptions as the Index Option for the Index Performance Strategy with 1-year Term using S&P 500® Index example, but
with a 50% Cap, 100% Participation Rate, and 20% Buffer. Assume that all Proxy Value inputs except the Index price stay constant throughout the Term. When calculating Proxy Value for the Index Performance Strategy with 3-year Term Index Options, the
Black Scholes model uses the Time remaining multiplied by three. Please note that these examples may differ from your actual results due to rounding.
Term Start Date
On the Term Start Date we calculate the beginning Proxy Value as follows.
|
Strike price
|
AMC = 1
|
OMC = 1.5
|
OMP = 0.80
|
|
Notional amount
|
AMC = 1
|
OMC = 1
|
OMP = 1
|
|
Index Value
|
1,000
|
||
|
Term TD return
|
NA
|
||
|
Interest rate
|
1.00%
|
||
|
Dividend yield
|
2.20%
|
||
|
Time remaining
|
1
|
||
|
Volatility
|
17.00%
|
13.00%
|
22.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 9.52%
|
OMC = 0.25%
|
OMP = 6.46%
|
Beginning Proxy Value = AMC – OMC – OMP = 9.52% - 0.25% - 6.46% = 2.82%
|
Month
|
Index Value
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
Term Start Date
|
1,000
|
9.52%
|
0.25%
|
6.46%
|
2.82%
|
$0.00
|
$10,000.00
|
End of month one with changes to Proxy Value inputs
Proxy Value inputs can result in a negative Daily Adjustment even with a positive return in the Index. As in the 1-year Term Index Option example,
assume the Index price increased to 1,010 by the end of month one. In addition, assume volatility decreased by 5% and dividend yield increased from 2.20% to 5%. We calculate the current Proxy Value as follows:
|
Strike price
|
AMC = 1
|
OMC = 1.5
|
OMP = 0.80
|
|
Notional amount
|
AMC = 1
|
OMC = 1
|
OMP = 1
|
|
Index price
|
1,010
|
||
|
Term TD return
|
1.00%
|
||
|
Interest rate
|
1.00%
|
||
|
Dividend yield
|
5.00%
|
||
|
Time remaining
|
0.97
|
||
|
Volatility
|
12.00%
|
8.00%
|
17.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 3.60%
|
OMC = 0.00%
|
OMP = 5.47%
|
Current Proxy Value = AMC – OMC – OMP = 3.60% - 0.00% - 5.47% = -1.87%
In this example the Index price increased since the Term Start Date, which generally increases the Proxy Value. We calculate the Daily Adjustment and Index Option
Value as follows.
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value) = (-1.87% - 2.82%) = -4.69%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 2.82% x (1 – 0.97) = 0.078%
|
= [(a) -4.69% + (b) 0.078%] x $10,000 = -$461.52
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + -$461.52 = $9,538.48
|
Month
|
Index Price
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
1
|
1,010
|
3.60%
|
0.00%
|
5.48%
|
-1.88%
|
-$461.52
|
$9,538.48
|
Term Start Date if 3-year Term Index Option is uncapped
This example uses the same assumptions as the prior Term Start Date example, but has no Cap. Because this 3-year Term Index Option is uncapped the OMC is zero and
we do not need to consider the volatility for this option.
On the Term Start Date we calculate the beginning Proxy Value as follows.
|
Strike price
|
AMC = 1
|
N/A
|
OMP = 0.80
|
|
Notional amount
|
AMC = 1
|
N/A
|
OMP = 1
|
|
Index Value
|
1,000
|
||
|
Term TD return
|
NA
|
||
|
Interest rate
|
1.00%
|
||
|
Dividend yield
|
2.20%
|
||
|
Time remaining
|
1
|
||
|
Volatility
|
17.00%
|
N/A
|
22.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 9.52%
|
OMC = 0.00%
|
OMP = 6.46%
|
Beginning Proxy Value = AMC – OMC – OMP = 9.52% - 0.00% - 6.46% = 3.07%
|
Month
|
Index Value
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
Term Start Date
|
1,000
|
9.52%
|
0.00%
|
6.46%
|
3.07%
|
$0.00
|
$10,000.00
|
EXAMPLE: INDEX PERFORMANCE STRATEGY WITH 6-YEAR TERM USING S&P 500® INDEX
This example uses the same assumptions as the Index Performance Strategy with 3-year Term using S&P 500® Index example, but has no Cap, a 140%
Participation Rate, and 10% Buffer. Assume that all Proxy Value inputs except the Index price stay constant throughout the Term. When calculating Proxy Value for the Index Performance Strategy with 6-year Term Index Options, the Black Scholes model
uses the Time remaining multiplied by six. Please note that these examples may differ from your actual results due to rounding.
Term Start Date
On the Term Start Date we calculate the beginning Proxy Value as follows.
|
Strike price
|
AMC = 1
|
N/A
|
OMP = 0.90
|
|
Notional amount
|
AMC = 1.4
|
N/A
|
OMP = 1
|
|
Index Value
|
1,000
|
||
|
Term TD return
|
NA
|
||
|
Interest rate
|
1.50%
|
||
|
Dividend yield
|
2.20%
|
||
|
Time remaining
|
1
|
||
|
Volatility
|
20.00%
|
N/A
|
23.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 21.71%
|
OMC = 0.00%
|
OMP = 16.27%
|
Beginning Proxy Value = AMC – OMC – OMP = 21.71% - 0.00% - 16.27% = 5.44%
|
Month
|
Index Value
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
Term Start Date
|
1,000
|
21.71%
|
0.00%
|
16.27%
|
5.44%
|
$0.00
|
$10,000.00
|
End of month one with changes to Proxy Value inputs
Proxy Value inputs can result in a negative Daily Adjustment even with a positive return in the Index. As in the 1-year Term Index Option example,
assume the Index price increased to 1,010 by the end of month one. In addition, assume volatility decreased by 5% and dividend yield increased from 2.20% to 5%. We calculate the current Proxy Value as follows:
|
Strike price
|
AMC = 1
|
N/A
|
OMP = 0.90
|
|
Notional amount
|
AMC = 1.4
|
N/A
|
OMP = 1
|
|
Index price
|
1,010
|
||
|
Term TD return
|
1.00%
|
||
|
Interest rate
|
1.50%
|
||
|
Dividend yield
|
5.00%
|
||
|
Time remaining
|
0.99
|
||
|
Volatility
|
15.00%
|
N/A
|
18.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 7.80%
|
OMC = 0.00%
|
OMP = 17.55%
|
Current Proxy Value = AMC – OMC – OMP = 7.80% - 0.00% - 17.55% = -9.75%
In this example the Index price increased since the Term Start Date, which generally increases the Proxy Value. We calculate the Daily Adjustment and Index Option
Value as follows.
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value) = (-9.75% - 5.44%) = -15.19%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 5.44% x (1 – 0.99) = 0.076%
|
= [(a) -15.19% + (b) 0.076%] x $10,000 = -$1,511.70
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + -$1,511.70 = $8,488.30
|
Month
|
Index Price
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
1
|
1,010
|
7.80%
|
0.00%
|
17.55%
|
-9.75%
|
-$1,511.70
|
$8,488.30
|
EXAMPLE: INDEX PERFORMANCE STRATEGY WITH 1-YEAR TERM USING EURO STOXX 50®
Assume you purchase a Contract and allocate your total initial Purchase Payment of $10,000 to the Index Option for the Index Performance Strategy 1-year Term using
EURO STOXX 50®. On the Term Start Date the Index Option Base is $10,000, the Cap is 15%, the Buffer is 10% and the Index Value is 1,000. Please note that these examples may differ from
your actual results due to rounding.
Term Start Date
On the Term Start Date we calculate the beginning Proxy Value as follows.
|
Strike price
|
AMC = 1
|
OMC = 1.15
|
OMP = 0.90
|
|
Index Value
|
1,000
|
||
|
Term TD return
|
NA
|
||
|
Interest rate
|
0.50%
|
||
|
Adjusted dividend yield
|
2.05%
|
||
|
Time remaining
|
1
|
||
|
Volatility
|
15.00%
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 5.17%
|
OMC = 1.24%
|
OMP = 2.37%
|
Beginning Proxy Value = AMC – OMC – OMP = 5.17% – 1.24% – 2.37% = 1.57%
|
Month
|
Index Value
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
Term Start Date
|
1,000
|
5.17%
|
1.24%
|
2.37%
|
1.57%
|
$0.00
|
$10,000.00
|
EXAMPLE: INDEX GUARD STRATEGY USING THE S&P 500® INDEX
Assume you purchase a Contract and allocate your total initial Purchase Payment of $10,000 to the Index Option with the Index Guard Strategy using S&P 500®
Index. On the Term Start Date the Index Option Base is $10,000, the Cap is 20%, the Floor is -10% and the Index Value is 1,000. Please note that these examples may differ from your actual results
due to rounding.
Term Start Date
On the Term Start Date we calculate the beginning Proxy Value as follows.
|
Strike price
|
AMC = 1.00
|
OMC = 1.20
|
AMP = 1.00
|
OMP = 0.90
|
|
Index Value
|
1,000
|
|||
|
Term TD return
|
NA
|
|||
|
Interest rate
|
0.50%
|
|||
|
Dividend yield
|
2.20%
|
|||
|
Time remaining
|
1
|
|||
|
Volatility
|
15.00%
|
15.00%
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 5.10%
|
OMC = 0.69%
|
AMP = 6.77%
|
OMP = 2.41%
|
Beginning Proxy Value = AMC – OMC – AMP + OMP = 5.10% – 0.69% – 6.77 + 2.41% = 0.04%
|
Month
|
Index Value
|
AMC
|
OMC
|
AMP
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
Term Start Date
|
1,000
|
5.10%
|
0.69%
|
6.77%
|
2.41%
|
0.04%
|
$0.00
|
$10,000.00
|
End of month three
Assume the Index price decreased to 950 by the end of month three. We calculate the current Proxy Value as follows:
|
Strike price
|
AMC = 1.00
|
OMC = 1.20
|
AMP = 1.00
|
OMP = 0.70
|
|
Index price
|
950
|
|||
|
Term TD return
|
-5.00%
|
|||
|
Interest rate
|
0.50%
|
|||
|
Dividend yield
|
2.20%
|
|||
|
Time remaining
|
0.75
|
|||
|
Volatility
|
15.00%
|
15.00%
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 2.50%
|
OMC = 0.15%
|
AMP = 8.68%
|
OMP = 3.09%
|
Current Proxy Value = AMC – OMC – AMP + OMP = 2.50% – 0.15% – 8.68% + 3.09% = -3.25%
We calculate the Daily Adjustment and Index Option Value as follows.
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value) = (-3.25% - 0.04%) = -3.28%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 0.04% x (1 - 0.75) = 0.0092%
|
= [(a) -3.29% + (b) 0.0092%] x $10,000 = -$327.32
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + -$327.32 =
$9,672.68
|
Month
|
Index Price
|
AMC
|
OMC
|
AMP
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
3
|
950
|
2.50%
|
0.15%
|
8.68%
|
3.09%
|
-3.25%
|
-$327.32
|
$9,672.68
|
EXAMPLE: INDEX PRECISION STRATEGY USING THE S&P 500® INDEX
Assume you purchase a Contract and allocate your total initial Purchase Payment of $10,000 to the Index Option with the Index Precision Strategy using S&P 500®
Index. On the Term Start Date the Index Option Base is $10,000, the Precision Rate is 8%, the Buffer is -10% and the Index Value is 1,000. Please note that these examples may differ from your actual
results due to rounding.
Term Start Date
On the Term Start Date we calculate the beginning Proxy Value as follows.
|
Strike price
|
AMBC = 1
|
OMP = 0.90
|
|
Index Value
|
1,000
|
|
|
Term TD return
|
NA
|
|
|
Interest rate
|
0.50%
|
|
|
Dividend yield
|
2.20%
|
|
|
Time remaining
|
1
|
|
|
Volatility
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMBC = 42.32%
|
OMP = 2.41%
|
Beginning Proxy Value = (Precision Rate x AMBC) – OMP = (8% x 42.32%) – 2.41% = 0.98%
|
Month
|
Index Value
|
AMBC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
Term Start Date
|
1,000
|
42.32%
|
2.41%
|
0.98%
|
$0.00
|
$10,000.00
|
End of month three
Assume the Index price increased to 1050 by the end of month three. We calculate the current Proxy Value as follows:
|
Strike price
|
AMBC = 1
|
OMP = 0.90
|
|
Index price
|
1,050
|
|
|
Index YTD return
|
5.00%
|
|
|
Interest rate
|
0.50%
|
|
|
Dividend yield
|
2.20%
|
|
|
Time remaining
|
0.75
|
|
|
Volatility
|
15.00%
|
|
|
Value of derivatives using Black Scholes
|
AMBC = 58.19%
|
OMP = 0.88%
|
Current Proxy Value = (Precision Rate x AMBC) – OMP = (8% x 58.19%) – 0.88% = 3.78%
We calculate the Daily Adjustment and Index Option Value as follows.
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value) = (3.78% - 0.98%) = 2.80%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 0.98% x (1 - 0.75) = 0.245%
|
= [(a) 2.80% + (b) 0.245%] x $10,000 = $304.51
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + $304.51 =
$10,304.51
|
Month
|
Index Price
|
AMBC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
3
|
1,050
|
58.19%
|
0.88%
|
3.78%
|
$304.51
|
$10,304.51
|
EXAMPLE: INDEX PROTECTION STRATEGY WITH CAP USING THE S&P 500® INDEX
Assume you purchase a Contract and allocate your total initial Purchase Payment of $10,000 to the Index Option with the Index Protection Strategy with Cap using
S&P 500® Index. On the Term Start Date the Index Option Base is $10,000, the Cap is 4% and the Index Value is 1,000. Please note that these examples may differ from your actual
results due to rounding.
Term Start Date
On the Term Start Date we calculate the beginning Proxy Value as follows.
|
Strike price
|
AMC = 1
|
OMC = 1.04
|
|
Index Value
|
1,000
|
|
|
Term TD return
|
NA
|
|
|
Interest rate
|
0.50%
|
|
|
Dividend yield
|
2.20%
|
|
|
Time remaining
|
1
|
|
|
Volatility
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 5.10%
|
OMC = 3.61%
|
Beginning Proxy Value = AMC – OMC = 5.10% – 3.61% = 1.49%
|
Month
|
Index Value
|
AMC
|
OMC
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
Term Start Date
|
1,000
|
5.10%
|
3.61%
|
1.49%
|
$0.00
|
$10,000.00
|
End of month three
Assume the Index price increased to 1050 by the end of month three. We calculate the current Proxy Value as follows:
|
Strike price
|
AMC = 1
|
OMC = 1.04
|
|
Index price
|
1,050
|
|
|
Index YTD return
|
5.00%
|
|
|
Interest rate
|
0.50%
|
|
|
Dividend yield
|
2.20%
|
|
|
Time remaining
|
0.75
|
|
|
Volatility
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 7.28%
|
OMC = 5.19%
|
Current Proxy Value = AMC – OMC = 7.28% – 5.19% = 2.09%
We calculate the Daily Adjustment and Index Option Value as follows.
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value) = (2.09% - 1.49%) = 0.60%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.49% x (1 - 0.75) = 0.37%
|
= [(a) 0.60% + (b) 0.373%] x $10,000 = $96.94
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + $96.94 =
$10,096.94
|
Month
|
Index Price
|
AMC
|
OMC
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
3
|
1,050
|
7.28%
|
5.19%
|
2.09%
|
$96.94
|
$10,096.94
|
EXAMPLE: INDEX PROTECTION STRATEGY WITH DPSC USING THE S&P 500® INDEX
Assume you purchase a Contract and allocate your total initial Purchase Payment of $10,000 to the Index Option with the Index Protection Strategy with DPSC using
S&P 500® Index. On the Term Start Date the Index Option Base is $10,000, the DPSC is 3% and the Index Value is 1,000. Please note that these examples may differ from your actual
results due to rounding.
Term Start Date
On the Term Start Date we calculate the beginning Proxy Value as follows.
|
Strike price
|
AMBC = 1
|
|
|
Index Value
|
1,000
|
|
|
Term TD return
|
NA
|
|
|
Interest rate
|
0.50%
|
|
|
Dividend yield
|
2.20%
|
|
|
Time remaining
|
1
|
|
|
Volatility
|
15.00%
|
|
|
Value of derivatives using Black Scholes
|
AMBC = 42.32%
|
Beginning Proxy Value = DPSC x AMBC = (3% x 42.32%) = 1.27%
|
Month
|
Index Value
|
AMBC
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
Term Start Date
|
1,000
|
42.32%
|
1.27%
|
$0.00
|
$10,000.00
|
End of month three
Assume the Index price increased to 1050 by the end of month three. We calculate the current Proxy Value as follows:
|
Strike price
|
AMBC = 1
|
|
|
Index price
|
1,050
|
|
|
Index YTD return
|
5.00%
|
|
|
Interest rate
|
0.50%
|
|
|
Dividend yield
|
2.20%
|
|
|
Time remaining
|
0.75
|
|
|
Volatility
|
15.00%
|
|
|
Value of derivatives using Black Scholes
|
AMBC = 58.19%
|
Current Proxy Value = DPSC x AMBC = (3% x 58.19%) = 1.75%
We calculate the Daily Adjustment and Index Option Value as follows.
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value) = (1.75% - 1.27%) = 0.48%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.27% x (1 - 0.75) = 0.317%
|
= [(a) 0.48% + (b) 0.317%] x $10,000 = $79.37
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + $79.37 =
$10,079.37
|
Month
|
Index Price
|
AMBC
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
3
|
1,050
|
58.19%
|
1.75%
|
$79.37
|
$10,079.37
|
EXAMPLE: INDEX PERFORMANCE STRATEGY WITH 1-YEAR TERM USING
ISHARES® MSCI EMERGING MARKETS ETF
ISHARES® MSCI EMERGING MARKETS ETF
Assume you purchase a Contract and allocate your total initial Purchase Payment of $10,000 to the Index Option for the Index Performance Strategy with 1-year Term
using iShares® MSCI Emerging Markets ETF. On the Term Start Date the Index Option Base is $10,000, the Cap is 15%, the Buffer is 10% and the Index Value is 1,000. Please note that these
examples may differ from your actual results due to rounding.
Term Start Date
On the Term Start Date we calculate the beginning Proxy Value as follows.
|
Strike price
|
AMC = 1
|
OMC = 1.15
|
OMP = 0.90
|
|
Index Value
|
1,000
|
||
|
Term TD return
|
NA
|
||
|
Interest rate
|
0.50%
|
||
|
Present value of dividends
|
20.95 (calculated below)
|
||
|
Time remaining
|
1
|
||
|
Volatility
|
15.00%
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 5.14%
|
OMC = 1.22%
|
OMP = 2.39%
|
Beginning Proxy Value = AMC – OMC – OMP = 5.14% – 1.22% – 2.39% = 1.53%
|
Month
|
Index Value
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
Term Start Date
|
1,000
|
5.14%
|
1.22%
|
2.39%
|
1.53%
|
$0.00
|
$10,000.00
|
Present value of dividends calculation:
|
First dividend forecasted amount
|
10
|
|
Time until first dividend forecasted date
|
0.25
|
|
Second dividend forecasted amount
|
11
|
|
Time until second dividend forecasted date
|
0.75
|
|
Interest rate
|
0.50%
|
Present Value of Dividends = (10 x 0.9988) + (11 x 0.9963)
Present Value of Dividends = 20.95
End of month three
Assume the Index price increased to 1,020 by the end of month three. We calculate the current Proxy Value as follows:
|
Strike price
|
AMC = 1
|
OMC = 1.15
|
OMP = 0.90
|
|
Index price
|
1,020
|
||
|
Index YTD return
|
2.00%
|
||
|
Interest rate
|
0.50%
|
||
|
Present value of dividends
|
10.99 (calculated below)
|
||
|
Time remaining
|
0.75
|
||
|
Volatility
|
15.00%
|
15.00%
|
15.00%
|
|
Value of derivatives using Black Scholes
|
AMC = 5.86%
|
OMC = 1.21%
|
OMP = 1.22%
|
Current Proxy Value = AMC – OMC – OMP = 5.86% – 1.21% – 1.22% = 3.42 %
In this example the Index price increased since the beginning of the year, which generally increases the Proxy Value. We calculate the Daily Adjustment and Index
Option Value as follows.
Daily Adjustment = [(a) change in Proxy Value + (b) proxy interest] x Index Option Base:
| (a) |
change in Proxy Value = (current Proxy Value – beginning Proxy Value) = (3.42% - 1.53%) = 1.90 %
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.53% x (1 - 0.75) = 0.38%
|
= [(a) 1.90 % + (b) 0.38%] x $10,000 = $227.91
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + $227.91 =
$10,227.91
|
Month
|
Index Price
|
AMC
|
OMC
|
OMP
|
Proxy Value
|
Daily Adjustment
|
Index Option Value
|
|
1
|
1,020
|
5.86%
|
1.21%
|
1.22%
|
3.42%
|
$227.91
|
$10,227.91
|
Present value of dividends calculation:
|
First dividend was already paid
|
|
|
Second dividend forecasted amount
|
11
|
|
Time until second dividend forecasted date
|
0.25
|
|
Interest rate
|
0.50%
|
Present value of dividends = 11 x 0.9988
Present value of dividends = 10.99