Attached files
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EXHIBIT – DAILY ADJUSTMENT CALCULATION
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We designed the Daily Adjustment to provide an Index Option Value on days other than the Index Effective Date or an Index Anniversary that reflects the change in market value of your allocation to each Index Performance Strategy Index Option. 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 this calculation is as follows:
Daily Adjustment = (current Proxy Value – beginning Proxy Value) x Index Option Base
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 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:
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an at-the-money call;
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an out-of-the-money call; and
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an out-of-the-money put.
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An Index Option’s Proxy Value = (at-the-money call) – (out-of-the-money call) – (out-of-the-money put)
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 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
This is an option to buy a position in the Index on the next Index Anniversary at the price of 1. On an Index Anniversary the at-the-money call’s value is equal to the Index’s current value divided by the Index’s 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
This is an option to buy a position in the Index on the next Index Anniversary at the price of 1 plus the Cap percentage. On an Index Anniversary the out-of-the-money call’s value is equal to the Index’s current value divided by the Index’s 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.
Out-of-the-money-put
This is an option to sell a position in the Index on the next Index Anniversary at the price of 1 minus the Buffer percentage. On an Index Anniversary the out-of-the-money put’s value is equal to 1 minus the Buffer percentage minus the quotient of the Index’s value on the last Index Anniversary (or the Index Effective Date if this is the first Index Anniversary) divided by the Index’s current value, the difference being no less than zero.
PROXY VALUE INPUTS
We calculate each hypothetical derivative investment daily using the Black Scholes model for valuing a European Option. The following inputs are used in the calculation.
Implied Volatility – The six-month implied volatility as provided daily by Bloomberg or another market source.
Dividend Yield – The average annual dividend yield over the most recent ten-year period, as set at the beginning of each calendar year. The dividend yield stays constant throughout the calendar year.
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Risk-free 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.
Time until expiration – The number of days remaining in the current Index Year divided by 365.
Current Price – The Index’s value at the end of the current Business Day divided by the Index’s value on the last Index Anniversary (or the Index Effective Date if this is before the first Index Anniversary).
Strike Price – This varies for each derivative investment as follows.
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For an at-the-money call the strike price is equal to 1.
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For an out-of-the-money call the strike price is equal to 1 plus the Cap percentage.
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For an out-of-the-money put the strike price is equal to 1 minus the Buffer percentage.
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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-the-money call, and OMP means out-the-money put.
Assume the Proxy Value inputs stayed constant during the first three months of the Index Year and that the Index value decreased to 950. On the Index Effective Date we calculate the beginning Proxy Value as follows.
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Strike price
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AMC = 1
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OMC = 1.18
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OMP = 0.90
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Index value
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1,000
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Current price
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1
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Risk-free rate
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0.50%
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Dividend yield
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2.20%
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Time until expiration
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1
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Implied volatility
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20.00%
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Value of derivatives using Black Scholes
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AMC = 7.05%
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OMC = 2.10%
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OMP = 4.04%
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Beginning Proxy Value = AMC - OMC – OMP = 7.05% – 2.10% – 4.04% = 0. 91%
Three months later
Similarly we calculate the current Proxy Value at the end of three months by using parameters from that date as follows.
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Strike price
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AMC = 1
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OMC = 1.18
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OMP = 0.90
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Index value
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950
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Current price
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0.95
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Risk-free rate
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0.50%
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Dividend yield
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2.20%
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Time until expiration
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0.75
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Implied volatility
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20.00%
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Value of derivatives using Black Scholes
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AMC = 4.02%
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OMC = 0.78%
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OMP = 4.61%
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Current Proxy Value = AMC - OMC – OMP = 4.02% – 0.78% – 4.61% = -1.37%
In this example the Index value decreased, which generally lowers the Proxy Value. We calculate the Daily Adjustment and Index Option Value as follows.
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Daily Adjustment = (current Proxy Value – beginning Proxy Value) x Index Option Base = (-1.37% – 0. 91%) x $10,000 = -$227.73
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Index Option Value = Index Option Base + Daily Adjustment = $10,000.00 + -$227.73 = $9,772.27
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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 example except the Index value and current price. 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.
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Month
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Index Value
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AMC
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OMC
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OMP
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Proxy Value
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Daily Adjustment
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Index Option Value
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Index Effective Date
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1,000
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7.05%
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2.10%
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4.04%
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0.91%
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$0.00
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$10,000.00
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1
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1,050
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9.52%
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3.05%
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2.52%
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3.95%
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$304.20
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$10,304.20
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2
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975
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5.34%
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1.27%
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4.12%
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-0.05%
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-$95.98
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$9,904.02
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3
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950
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4.02%
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0.78%
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4.61%
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-1.37%
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-$227.73
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$9,772.27
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4
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925
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2.85%
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0.43%
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5.19%
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-2.76%
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-$367.35
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$9,632.65
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5
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850
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0.90%
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0.07%
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8.70%
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-7.87%
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-$877.67
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$9,122.33
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6
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910
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1.83%
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0.16%
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4.95%
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-3.29%
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-$420.08
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$9,579.92
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7
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980
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3.84%
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0.41%
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2.02%
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1.41%
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$49.92
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$10,049.92
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8
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1,015
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5.09%
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0.51%
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0.93%
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3.66%
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$274.53
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$10,274.53
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9
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1,100
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10.55%
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1.50%
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0.09%
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8.96%
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$804.38
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$10,804.38
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10
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1,125
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12.48%
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1.53%
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0.01%
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10.94%
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$1,002.90
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$11,002.90
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11
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1,095
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9.50%
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0.29%
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0.00%
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9.21%
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$830.12
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$10,830.12
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1st Index Anniversary
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1,080
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8.00%
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0.00%
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0.00%
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8.00%
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$800.00
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$10,800.00
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Notice how at the end of month twelve the Index Option Value increased 8%. The Proxy Value equals the Credit percent on the Index Anniversary.