| EXHIBIT – DAILY ADJUSTMENT CALCULATION |
We designed the Daily Adjustment to provide an Index Option Value for the Index Performance Strategy Index Options on days other than the Index Effective Date or an Index Anniversary.
The Daily Adjustment has two components, the change in Proxy Value and accumulated proxy interest. The change in Proxy Value represents the current market 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 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 change in Proxy Value and the proxy interest estimates the present value of positive or negative Performance Credits on the next Index Anniversary.
You should note that even if your selected Index(s) experience positive growth, their Daily Adjustments may be negative because of other market conditions, such as the expected volatility of Index prices and interest rates.
The formula for the calculation of the Daily Adjustment is as follows:
Daily Adjustment = (a) change in Proxy Value plus (b) proxy interest
(a) change in Proxy Value = (current Proxy Value – beginning Proxy Value) x Index Option Base
(b) proxy interest = proxy interest rate x (1 - time remaining) x Index Option Base
proxy interest rate = 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 time remaining is equal to the number of days remaining in the Index Year divided by 365.
The Proxy Value tracks three hypothetical derivative investments (call and put options) that we designed to mimic the market value of your allocation to an Index Performance Strategy Index Option. We calculate a Proxy Value for each of your selected Index Performance Strategy Index Options.
The Proxy Value has three components:
| · | an at-the-money call (AMC); |
| · | an out-of-the-money call (OMC); and |
| · | an out-of-the-money put (OMP). |
An Index Option’s Proxy Value = (AMC) – (OMC) – (OMP)
We designed the two call options to value the potential for Index gains up to the Cap. We designed the put option to value the potential for Index losses below the Buffer. It is important to note that the put option will almost always reduce the Daily Adjustment, even when the current Index value is higher than it was at the beginning of the Index Year. 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 Index value is lower than it was at the beginning of the Index Year.
On the Index Anniversary, the current Proxy Value for an Index Option is equal to its Performance Credit as discussed in section 7, Index Options – Determining the Index Option Value under the Index Performance Strategy. A more complete description of each derivative follows.
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 at-the-money call’s value is equal to the current Index value 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.
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 percentage). On an Index Anniversary the out-of-the-money call’s value is equal to the current Index value 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 percentage, the difference being no less than zero.
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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 minus the Buffer percentage). On an Index Anniversary the out-of-the-money put’s value is equal to one minus the Buffer percentage 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 value, the difference being no less than zero.
Proxy interest is the amount of interest earned based upon the Index Option Base using simple interest throughout the Index Year. The proxy interest and the proxy interest rate can be positive or negative. The proxy interest rate is set at the beginning of each Index Year to be equal to the beginning Proxy Value. The proxy interest rate provides compensation for the cost of the Proxy Investment at the beginning of the Index Year (on the Index Effective Date for the first Index Year, and on each subsequent Index Anniversary), which is equal to the beginning Proxy Value.
PROXY VALUE CALCULATION
Throughout the Index Year, we calculate each hypothetical derivative investment 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
Index – The Index value 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 values 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 dividend yield remains constant throughout the calendar year. Since dividends typically reduce Index values, a higher dividend yield will lead to a lower expected Index value.
Strike price – This varies for each derivative investment as follows.
| · | For an at-the-money call the strike price is equal to 1. |
| · | For an out-of-the-money call the strike price is equal to 1 plus the Cap percentage. |
| · | For an out-of-the-money put the strike price is equal to 1 minus the Buffer percentage. |
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 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 volatility 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.
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EXAMPLE
Assume you purchase a Contract and allocate your total initial Purchase Payment of $10,000 to the S&P 500® Index under the Index Performance Strategy. On the Index Effective Date the Index Option Base is $10,000, the Cap is 18%, the Buffer is 10% and the Index value is 1,000. In this example AMC means at-the-money call, OMC means out-of-the-money call, and OMP means out-of-the-money put. Assume that all Proxy Value inputs except the Index value stay constant throughout the year.
Index Effective Date
On the Index Effective Date we calculate the beginning Proxy Value as follows.
| Strike price | AMC = 1 | OMC = 1.18 | OMP = 0.90 |
| Index value | 1,000 | ||
| Index price | 1 | ||
| Interest rate | 0.50% | ||
| Dividend yield | 2.20% | ||
| Time remaining | 1 | ||
| Volatility | 20.00% | ||
| Value of derivatives using Black Scholes | AMC = 7.05% | OMC = 2.10% | OMP = 4.04% |
Beginning Proxy Value = AMC - OMC – OMP = 7.05% – 2.10% – 4.04% = 0. 91%
| Month | Index Value | AMC | OMC | OMP | Proxy Value | Daily Adjustment | Index Option Value |
| Index Effective Date | 1,000 | 7.05% | 2.10% | 4.04% | 0.91% | $0.00 | $10,000.00 |
End of month one
Assume the Index value increased to 1,010 by the end of month one. We calculate the current Proxy Value as follows:
| Strike price | AMC = 1 | OMC = 1.18 | OMP = 0.90 |
| Index value | 1,010 | ||
| Index price | 1.01 | ||
| Interest rate | 0.50% | ||
| Dividend yield | 2.20% | ||
| Time remaining | 0.92 | ||
| Volatility | 20.00% | ||
| Value of derivatives using Black Scholes | AMC = 7.29% | OMC = 2.09% | OMP = 3.44% |
Current Proxy Value = AMC - OMC – OMP = 7.29% – 2.09% – 3.44% = 1.76%
In this example the Index value 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 plus (b) Proxy Interest = $84.78 + $7.60 = $92.38
(a) Change in Proxy Value = (current Proxy Value – beginning Proxy Value) x Index Option Base = (1.76% - 0.91%) x $10,000 = $84.78
(b) Proxy Interest = Proxy Interest Rate x (1 - Time remaining) x Index Option Base = 0.91% x 0.083 x $10,000 = $7.60
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + $92.38 = $10,092.38 |
| Month | Index Value | AMC | OMC | OMP | Proxy Value | Daily Adjustment | Index Option Value |
| 1 | 1,010 | 7.29% | 2.09% | 3.44% | 1.76% | $92.38 | $10,092.38 |
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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 value increased to 1,010 by the end of month one. In addition, assume volatility decreased from 20% to 5% and Dividend yield increased from 2.20% to 5%. We calculate the current Proxy Value as follows:
| Strike price | AMC = 1 | OMC = 1.18 | OMP = 0.90 |
| Index value | 1,010 | ||
| Index price | 1.01 | ||
| 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 value 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 plus (b) Proxy Interest = -$30.45 + $7.60 = -$22.86
(a) Change in Proxy Value = (current Proxy Value – beginning Proxy Value) x Index Option Base = (0.61% - 0.91%) x $10,000 = -$30.45
(b) Proxy Interest = Proxy Interest Rate x (1 - Time remaining) x Index Option Base = 0.91% x 0.083 x $10,000 = $7.60
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + -$22.86 = $9,977.14 |
| Month | Index Value | AMC | OMC | OMP | Proxy Value | Daily Adjustment | Index Option Value |
| 1 | 1,010 | 0.72% | 0.00% | 0.12% | 0.61% | -$22.86 | $9,977.14 |
End of month three
Assume the Index value decreased to 950 by the end of month three. We calculate the current Proxy Value as follows:
| Strike price | AMC = 1 | OMC = 1.18 | OMP = 0.90 |
| Index value | 950 | ||
| Index price | 0.95 | ||
| Interest rate | 0.50% | ||
| Dividend yield | 2.20% | ||
| Time remaining | 0.75 | ||
| Volatility | 20.00% | ||
| Value of derivatives using Black Scholes | AMC = 4.02% | OMC = 0.78% | OMP = 4.61% |
Current Proxy Value = AMC - OMC – OMP = 4.02% – 0.78% – 4.61% = -1.37%
In this example the Index value 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 plus (b) proxy interest = -$227.73 + $22.79 = -$204.94 |
(a) change in Proxy Value = (current Proxy Value – beginning Proxy Value) x Index Option Base = (-1.37% - 0.91%) x $10,000 = -$227.73
(b) proxy interest = proxy interest rate x (1 - time remaining) x Index Option Base = 0.91% x 0.25 x $10,000 = $22.79
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + -$204.94 = $9,795.06 |
| Month | Index Value | AMC | OMC | OMP | Proxy Value | Daily Adjustment | Index Option Value |
| 3 | 950 | 4.02% | 0.78% | 4.61% | -1.37% | -$204.94 | $9,795.06 |
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End of month six
Assume the Index value decreased to 910 by the end of month six. We calculate the current Proxy Value as follows:
| Strike price | AMC = 1 | OMC = 1.18 | OMP = 0.90 |
| Index value | 910 | ||
| Index price | 0.91 | ||
| Interest rate | 0.50% | ||
| Dividend yield | 2.20% | ||
| Time remaining | 0.50 | ||
| Volatility | 20.00% | ||
| Value of derivatives using Black Scholes | AMC = 1.83% | OMC = 0.16% | OMP = 4.95% |
Current Proxy Value = AMC - OMC – OMP = 1.83% – 0.16% – 4.95% = -3.29%
In this example the Index value 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 plus (b) proxy interest = -$420.08 + $45.58 = -$374.50 |
(a) change in Proxy Value = (current Proxy Value – beginning Proxy Value) x Index Option Base = (-3.29% - 0.91%) x $10,000 = -$420.08
| (b) proxy interest = proxy interest rate x (1 - time remaining) x Index Option Base = 0.91% x 0.5 x $10,000 = $45.58 |
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + -$374.50 = $9,625.50
| Month | Index Value | AMC | OMC | OMP | Proxy Value | Daily Adjustment | Index Option Value |
| 6 | 910 | 1.83% | 0.16% | 4.95% | -3.29% | -$374.50 | $9,625.50 |
End of month eleven
Assume the Index value increased to 1095 by the end of month eleven. We calculate the current Proxy Value as follows:
| Strike price | AMC = 1 | OMC = 1.18 | OMP = 0.90 |
| Index value | 1095 | ||
| Index price | 1.095 | ||
| Interest rate | 0.50% | ||
| Dividend yield | 2.20% | ||
| Time remaining | 0.08 | ||
| Volatility | 20.00% | ||
| Value of derivatives using Black Scholes | AMC = 9.50% | OMC = 0.29% | OMP = 0.00% |
Current Proxy Value = AMC - OMC – OMP = 9.50% – 0.29% – 0.00% = 9.21%
In this example the Index value 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 plus (b) proxy interest = $830.12 + $83.57 = $913.69 |
(a) change in Proxy Value = (current Proxy Value – beginning Proxy Value) x Index Option Base = (9.21% - 0.91%) x $10,000 = $830.12
| (b) proxy interest = proxy interest rate x (1 - time remaining) x Index Option Base = 0.91% x 0.917 x $10,000 = $83.57 |
Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + $913.69 = $10,913.69 |
| Month | Index Value | AMC | OMC | OMP | Proxy Value | Daily Adjustment | Index Option Value |
| 11 | 1,095 | 9.50% | 0.29% | 0.00% | 9.21% | $913.69 | $10,913.69 |
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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 values. Note that all Proxy Value inputs used are the same as in the above 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 the product fee and contract maintenance charge.
| Month | Index Value | AMC | OMC | OMP | Proxy Value | Daily Adjustment | Index Option Value |
| Index Effective Date | 1,000 | 7.05% | 2.10% | 4.04% | 0.91% | $0.00 | $10,000.00 |
| 1 | 1,010 | 7.29% | 2.09% | 3.44% | 1.76% | $92.38 | $10,092.38 |
| 2 | 975 | 5.34% | 1.27% | 4.12% | -0.05% | -$80.78 | $9,919.22 |
| 3 | 950 | 4.02% | 0.78% | 4.61% | -1.37% | -$204.94 | $9,795.06 |
| 4 | 925 | 2.85% | 0.43% | 5.19% | -2.76% | -$336.96 | $9,663.04 |
| 5 | 850 | 0.90% | 0.07% | 8.70% | -7.87% | -$839.69 | $9,160.31 |
| 6 | 910 | 1.83% | 0.16% | 4.95% | -3.29% | -$374.50 | $9,625.50 |
| 7 | 980 | 3.84% | 0.41% | 2.02% | 1.41% | $103.09 | $10,103.09 |
| 8 | 1,015 | 5.09% | 0.51% | 0.93% | 3.66% | $335.31 | $10,335.31 |
| 9 | 1,100 | 10.55% | 1.50% | 0.09% | 8.96% | $872.75 | $10,872.75 |
| 10 | 1,125 | 12.48% | 1.53% | 0.01% | 10.94% | $1,078.87 | $11,078.87 |
| 11 | 1,095 | 9.50% | 0.29% | 0.00% | 9.21% | $913.69 | $10,913.69 |
| 1st Index Anniversary | 1,080 | 8.00% | 0.00% | 0.00% | 8.00% | $800.00 | $10,800.00 |
Notice how at the end of month twelve the Index Option Value increased 8%. The Proxy Value equals the Performance Credit percentage on the Index Anniversary.
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