EX-99.B 4 ex99b.htm DAILY ADJUSTMENT CALCULATION
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 Performance Strategy and Index Guard Strategy on Business Days other than the Index Effective Date or an Index Anniversary. The Daily Adjustment approximates the Index Option Value on the next Index Anniversary, adjusting for:
(i) any Index gains during the Index Year subject to the Precision Rate or Cap 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 next Index Anniversary. 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 Index Year)
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 at the beginning of the Index Year (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 first day of the current Index Year.
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 next Index Anniversary, the Index Value is greater than or equal to the Index Value on the last Index Anniversary (or the Index Effective Date if this is the first Index Anniversary), 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 option 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 last Index Anniversary. This is because the risk that the Index Value could be lower on the next Index Anniversary is present to some extent whether or not the current Index price on a Business Day is lower than the Index Value on the last Index Anniversary.
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 last Index Anniversary. 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.
                                                                               Allianz Index Advantage®                                                  IXA-010b (__/2019)
Exhibit 99(b)
1

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 last Index Anniversary. This is because the risk that the Index Value could be lower on the next Index Anniversary is present to some extent whether or not the current Index price on a Business Day is lower than the Index Value on the last Index Anniversary.
DERIVATIVE DESCRIPTIONS
At-the-money binary call (AMBC)
This is an option to buy a position in the Index on the next Index Anniversary at the strike price of one. On an Index Anniversary 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 last Index Anniversary (or the Index Effective Date if this is the first Index Anniversary), or zero otherwise.
At-the-money call (AMC)
This is an option to buy a position in the Index on the next Index Anniversary at the strike price of one. On an Index Anniversary the AMC's value is equal to the current Index price on a Business Day divided by the Index Value on the last Index Anniversary (or the Index Effective Date if this is the first Index Anniversary), 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 next Index Anniversary at the strike price of one. On an Index Anniversary the AMP's value is equal to one minus the quotient of the Index Value on the last Index Anniversary (or the Index Effective Date if this is the first Index Anniversary) 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 next Index Anniversary at the strike price of (one plus the Cap). On an Index Anniversary the OMC's value is equal to the current Index price on a Business Day divided by the Index Value on the last Index Anniversary (or the Index Effective Date if this is the first Index Anniversary), then minus the sum of one plus the Cap, the difference being no less than zero.
Out-of-the-money-put (OMP)
This is an option to sell a position in the Index on the next Index Anniversary at the strike price of (one either minus the Buffer or plus the Floor, depending on the Index Option). On an Index Anniversary 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 last Index Anniversary (or the Index Effective Date if this is the first Index Anniversary) divided by the current Index price on a Business Day, the difference being no less than zero.
CALCULATING PROXY INTEREST
The proxy interest is an amount of interest that is earned to provide compensation for the cost of the Proxy Investment at the beginning of the Index Year. The proxy interest is approximated by the value of amortizing the cost of the Proxy Investment over the Index Year 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 an Index. The time remaining during an Index Year is equal to the number of days remaining in the Index Year divided by 365. The proxy interest may be significantly different from current interest rates available on interest bearing investments.
PROXY VALUE CALCULATION
Throughout the Index Year, on Business Days other than the Index Effective Date or an Index Anniversary, we calculate each hypothetical derivatives 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.
                                                                               Allianz Index Advantage®                                                  IXA-010b (__/2019)
Exhibit 99(b)
2

PROXY VALUE INPUTS
Index YTD return – The Index price at the end of the current Business Day divided by the Index Value on the last Index Anniversary (or the Index Effective Date if this is before the first Index Anniversary). 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.
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 the strike price is equal to 1 plus the Cap.
·
For an OMP the strike price is equal to 1 minus the Buffer.
Interest rate – 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 Index Anniversary to the time of calculation
Time remaining – The number of days in the Index Year from the next Index Anniversary to the time of the calculation divided by 365.
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 next Index Anniversary. 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.
                                                                               Allianz Index Advantage®                                                  IXA-010b (__/2019)
Exhibit 99(b)
3

EXAMPLE: INDEX PERFORMANCE STRATEGY WITH 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 Performance Strategy using the S&P 500® Index. On the Index Effective 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 year. Please note that these examples may differ from your actual results due to rounding.
Index Effective Date
On the Index Effective Date we calculate the beginning Proxy Value as follows.
Strike price
AMC = 1
OMC = 1.12
OMP = 0.90
Index Value
1,000
   
Index YTD 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
Index Effective 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
   
Index YTD 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 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) = (1.74% - 1.03%) = 0.71%
(b)
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.03% x (1 - 0.92) = 0.083%
= [(a) 0.71% + (b) 0.083%] 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

                                                                               Allianz Index Advantage®                                                  IXA-010b (__/2019)
Exhibit 99(b)
4

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
   
Index YTD 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 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) = (0.61% - 1.03%)  = -0.42%
(b)
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.03% x (1 - 0.92) = 0.083%
= [(a) -0.42% + (b) 0.083%] 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
   
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
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) = 0.25%
= [(a) -2.14% + (b) 0.25%] 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

                                                                               Allianz Index Advantage®                                                  IXA-010b (__/2019)
Exhibit 99(b)
5

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
   
Index YTD 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) = 0.52%
= [(a) -3.91% + (b) 0.52%] 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) = 0.95%
= [(a) 7.47% + (b) 0.95%] 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

                                                                               Allianz Index Advantage®                                                  IXA-010b (__/2019)
Exhibit 99(b)
6

The following table shows for each month during an Index Year 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 Index Year. In reality your Index Option Base changes throughout the year 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
Index Effective 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
1st Index Anniversary
1,080
         
$10,800.00

                                                                               Allianz Index Advantage®                                                  IXA-010b (__/2019)
Exhibit 99(b)
7

EXAMPLE: INDEX PERFORMANCE STRATEGY WITH THE EURO STOXX 50®
Assume you purchase a Contract and allocate your total initial Purchase Payment of $10,000 to the Index Option with the Index Performance Strategy using the EURO STOXX 50®. On the Index Effective 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.
Index Effective Date
On the Index Effective Date we calculate the beginning Proxy Value as follows.
Strike price
AMC = 1
OMC = 1.15
OMP = 0.90
Index Value
1,000
   
Index YTD 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
Index Effective 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%
                                                                               Allianz Index Advantage®                                                  IXA-010b (__/2019)
Exhibit 99(b)
8

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
   
Index YTD 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 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) = (1.09% - 1.57%)  = -0.48%
(b)
proxy interest = beginning Proxy Value x (1 - Time remaining) = 1.57% x (1 - 0.92) = 0.083%
= [(a) -0.48% + (b) 0.083%] 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%
                                                                               Allianz Index Advantage®                                                  IXA-010b (__/2019)
Exhibit 99(b)
9

EXAMPLE: INDEX GUARD STRATEGY WITH 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 the S&P 500® Index. On the Index Effective 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.
Index Effective Date
On the Index Effective 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
     
Index YTD 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
Index Effective 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
     
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
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%) = -3.29%
(b)
proxy interest = beginning Proxy Value x (1 - Time remaining) = 0.04% x (1 - 0.75) = 0.092%
= [(a) -3.29% + (b) 0.092%] 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

                                                                               Allianz Index Advantage®                                                  IXA-010b (__/2019)
Exhibit 99(b)
10

EXAMPLE: INDEX PRECISION STRATEGY WITH 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 the S&P 500® Index. On the Index Effective 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.
Index Effective Date
On the Index Effective Date we calculate the beginning Proxy Value as follows.
Strike price
AMBC = 1
OMP = 0.90
Index Value
1,000
 
Index YTD 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
Index Effective 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%) = 0.71%
(b)
proxy interest = beginning Proxy Value x (1 - Time remaining) = 0.98% x (1 - 0.75) = 0.245%
= [(a) 0.71% + (b) 0.245%] x $10,000 = $304.53
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + $304.53 = $10,304.53
Month
Index Price
AMBC
OMP
Proxy Value
Daily Adjustment
Index Option Value
3
1,050
58.19%
0.88%
3.78%
$304.53
$10,304.53


                                                                               Allianz Index Advantage®                                                  IXA-010b (__/2019)
Exhibit 99(b)
11