Attached files
| file | filename |
|---|---|
| S-1 - INDEX ADVANTAGE S-1 APRIL 2021 - ALLIANZ LIFE INSURANCE CO OF NORTH AMERICA | indexadvsapr2021.htm |
| EX-24.(C) - POWER OF ATTORNEY - ALLIANZ LIFE INSURANCE CO OF NORTH AMERICA | poa.htm |
| EX-23.(B) - CONSENT OF COUNSEL - ALLIANZ LIFE INSURANCE CO OF NORTH AMERICA | counselconsent.htm |
| EX-23.(A) - CONSENT OF AUDITOR - ALLIANZ LIFE INSURANCE CO OF NORTH AMERICA | auditorconsent.htm |
Exhibit 99(b) 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, and/or Participation
Rate or
(ii) either any Index losses greater than the Buffer or any Index losses down to the Floor.
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.
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.
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 average annual dividend
yield as provided by Bloomberg or another market source over the most recent ten-year period, as set at the beginning of each calendar year. The average is defined as the sum of the recent ten‑year dividend yield and divide by 10. The dividend yield
is a percentage calculated by the dividends divided by the index at the time the dividend was paid throughout the year. The dividend yield remains constant throughout the calendar year. 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. We add to the EURO STOXX 50®
dividend yield a difference in interest rates between the annual effective yield of a current six-month U.S. Constant Maturity Treasury Rate and the current six-month Euribor Rate, minus the covariance of EURO STOXX 50® and the exchange
rate. The covariance is the product of the correlation of euros to dollars exchange rate and EURO STOXX 50®, the six-month volatility of EURO STOXX 50®, and the six-month volatility of the euros to dollars 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 – For 1-year Term Index
Options we use the annual effective yield of a current six-month U.S. constant maturity treasury bond as provided daily by Bloomberg or another market source. The interest rate is used to present value the strike price from the next Term End Date to
the time of calculation. For 3-year and 6-year Term Index Options, every Business Day we use the annual effective yield for the treasury with a maturity equal to the length of time remaining during the Term. We approximate this yield by linearly
interpolating between two constant maturity treasury rates: a) the constant maturity treasury rate with closest available maturity to, but before the Term End Date, and b) the constant maturity treasury rate with closest available maturity to, but
after the Term End Date.
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 Bloomberg or another market source. Direct sources of volatility are generally not available, because options in the marketplace generally do not directly align with inputs of the proxy investments.
We approximate the volatility by linearly interpolating between two implied volatilities of at-the-money options. Implied
volatilities are determined using the Black Scholes model for European Options based upon daily option prices from Bloomberg or another market source. The two at-the-money options used are the at-the-money option with the closest available maturity
before and closest available maturity after the Term End Date. 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.
For 3-year and 6-year Term Index Options we use out-of-the-money options to adjust volatility based on the Strike prices of the AMC,
OMC and OMP. The volatility used for these Index Options is based on an extrapolation between the at-the-money volatility described above and the volatility of an out-of-the-money option. If the strike price is greater than the Term TD return, we
will extrapolate using the 20% OMC, otherwise we will use the 20% OMP. We approximate the volatility of the out-of-the-money option by using: a) the 20% OMC or OMP with closest available maturity to, but before the Term End Date, and b) the 20% OMC
or OMP with closest available maturity to, but after the Term End Date. For 3-year Term Index Options, we assume volatility is flat after the strike price is 30% higher than the at-the-money option. For 6-year Term Index Options, we assume volatility
is flat after the strike price is 60% higher than the at-the-money option. Adjustments made for the level of Strike price will not lower the volatility below 5%.
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%
|
||
|
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%
|
||
|
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 5% 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
|
5.00%
|
||
|
VALUE OF DERIVATIVES USING BLACK SCHOLES
|
AMC = 0.72%
|
OMC = 0.00%
|
OMP = 0.12%
|
Current Proxy Value = AMC – OMC – OMP = 0.72% – 0.00% – 0.12% = 0.61%
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) = (0.61% - 1.03%) = -0.42%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.03% x (1 - 0.92) = 0.086%
|
= [(a) -0.42% + (b) 0.086%] x $10,000 = -$33.79
Index Option Value =
Index Option Base + Daily Adjustment = $10,000.00 + -$33.79 = $9,966.21
|
MONTH
|
INDEX PRICE
|
AMC
|
OMC
|
OMP
|
PROXY VALUE
|
DAILY ADJUSTMENT
|
INDEX OPTION VALUE
|
|
1
|
1,010
|
0.72%
|
0.00%
|
0.12%
|
0.61%
|
-$33.79
|
$9,966.21
|
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%
|
||
|
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%
|
||
|
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%
|
||
|
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. Note that Participation Rates are only included on 3-year and 6-year Term Index Options available to Allianz Index Advantage® Contracts and Allianz Index Advantage
Income® Contracts issued on or after April 30, 2021. Allianz Index Advantage® Contracts and Allianz Index Advantage Income® Contracts issued before April 30, 2021, and Allianz Index Advantage® NF Contracts
and Allianz Index Advantage® ADV Contracts do not have a Participation Rate on 3-year Term Index Options. However, when the Participation Rate is 100%, as used here, there is no difference in the Proxy Value calculation between 3-year Term
Index Options without a Participation Rate and 3-year Term Index Options with a Participation Rate. 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 is uncapped, has a 140% Participation Rate, and a 10% Buffer. Note that the Index Performance Strategy with 6-Year Term Index Options are only available to Allianz Index Advantage® Contracts and Allianz Index Advantage Income®
Contracts issued on or after April 30, 2021. Allianz Index Advantage® Contracts and Allianz Index Advantage Income® Contracts issued before April 30, 2021, and Allianz Index Advantage® NF Contracts and Allianz Index
Advantage® ADV Contracts do not offer 6-year Term Index Options. 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% (AS CALCULATED BELOW)
|
||
|
TIME REMAINING
|
1
|
||
|
VOLATILITY
|
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
|
Assumptions for adjusted dividend yield:
|
EURO STOXX 50® DIVIDEND YIELD
|
2.20%
|
|
ANNUAL EFFECTIVE YIELD OF SIX-MONTH U.S. CONSTANT MATURITYTREASURY RATE
|
0.50%
|
|
ANNUAL EFFECTIVE YIELD OF SIX-MONTH EURIBOR RATE
|
0.25%
|
|
SIX MONTH VOLATILITY OF EURO STOXX 50®
|
15.00%
|
|
SIX MONTH VOLATILITY OF EXCHANGE RATE (EUROS/DOLLARS)
|
6.75%
|
|
CORRELATION OF EXCHANGE RATE AND EURO STOXX 50®
|
0.4
|
Adjusted dividend yield = 2.20% + (0.50% - 0.25%) – (15% x 6.75% x 0.4)
Adjusted dividend yield = 2.05%
End of month one with changes to adjusted dividend yield
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 the annual effective yield of six-month Euribor Rate went from 0.25% to 0.10%, the exchange rate volatility increased from 6.75% to 15%, and the
correlation of exchange rate and EURO STOXX 50® went from 0.4 to -0.8. We calculate the current Proxy Value as follows:
|
STRIKE PRICE
|
AMC = 1
|
OMC = 1.15
|
OMP = 0.90
|
|
INDEX PRICE
|
1,010
|
||
|
TERM TD RETURN
|
1.00%
|
||
|
INTEREST RATE
|
0.50%
|
||
|
ADJUSTED DIVIDEND YIELD
|
4.40% (AS CALCULATED BELOW)
|
||
|
TIME REMAINING
|
0.92
|
||
|
VOLATILITY
|
15.00%
|
||
|
VALUE OF DERIVATIVES USING BLACK SCHOLES
|
AMC = 4.45%
|
OMC = 0.93%
|
OMP = 2.43%
|
Beginning Proxy Value = AMC – OMC – OMP = 4.45% – 0.93% – 2.43% = 1.09%
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) = (1.09% - 1.57%) = -0.48%
|
| (b) |
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.57% x (1 - 0.92) = 0.13%
|
= [(a) -0.48% + (b) 0.13%] x $10,000 = -$34.98
Index Option
Value = Index Option Base + Daily Adjustment = $10,000.00 + -$34.98 = $9,965.02
|
MONTH
|
INDEX PRICE
|
AMC
|
OMC
|
OMP
|
PROXY VALUE
|
DAILY ADJUSTMENT
|
INDEX OPTION VALUE
|
|
1
|
1,010
|
4.45%
|
0.93%
|
2.43%
|
1.09%
|
-$34.98
|
$9,965.02
|
Assumptions for adjusted dividend yield:
|
EURO STOXX 50® DIVIDEND YIELD
|
2.20%
|
|
ANNUAL EFFECTIVE YIELD OF SIX-MONTH U.S. CONSTANT MATURITYTREASURY RATE
|
0.50%
|
|
ANNUAL EFFECTIVE YIELD OF SIX-MONTH EURIBOR RATE
|
0.10%
|
|
SIX MONTH VOLATILITY OF EURO STOXX 50®
|
15.00%
|
|
SIX MONTH VOLATILITY OF EXCHANGE RATE (EUROS/DOLLARS)
|
15.00%
|
|
CORRELATION OF EXCHANGE RATE AND EURO STOXX 50®
|
-0.8
|
Adjusted dividend yield = 2.20% + (0.50% - 0.10%) – (15% x 15% x -0.8)
Adjusted dividend yield = 4.40%
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%
|
|||
|
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%
|
|||
|
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%
|
|
|
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 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%
|
||
|
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%
|
||
|
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