35 lines
2.1 KiB
Plaintext
35 lines
2.1 KiB
Plaintext
Gopter 32: Structured Products 597
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Cash value of SIS $10 + $10 x 1.15 x ($MID - 166.10) / 166.10
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where
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Guarantee price = $10
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Underlying index: S&P Midcap 400 ($MID)
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Striking price: 166.10
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Participation rate: 115% of the increase of $MID above 166.10
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SIS matured seven years later, on June 2, 2000. At the time of issuance, seven-year
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interest rates were about 5.5%, so the "money in the bank" formula shows that one
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could have made about 4.7 points on a $10 investment, just by utilizing risk-free gov
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ernment securities:
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Money in the bank= 10 x e0-055 x 7 = 14.70
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We can't simply say that the cost of the imbedded call was 4. 7 points, though, because
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the participation rate is not 100% - it's greater. So we need to find out the Final Value
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of $MID that results in the cash value being equal to the "money in the bank" result.
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Using the cash value formula and inserting all the terms except the final value of
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$MID, we have the following equation. Note: $MIDMIB stands for the value of $MID
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that results in the "money in the bank" cash value, as computed above.
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14.70 = 10 + 10 X 1.15 X ($MIDMIB 166.10) I 166.10
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Solving for $MIDMIB' we get a value of 233.98. Now, convert this to a percent
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gain of the striking price:
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Imbedded call price = 233.98 I 166.10 - 1 = 0.4087
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Hence, the imbedded call costs 40.87% of the guarantee price. In this example,
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where the guarantee price was $10, that means the imbedded call cost $4.087.
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Thus, a more generalized formula for the value of the imbedded call can be
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construed from this example. This formula only works, though, where the participa
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tion rate is a fixed percentage of the strike price.
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Imbedded call value= Guarantee price x (Final Index ValueMIB / Striking Price - 1)
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Final Index ValueMIB is the final index price that results in the cash value
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being equal to the "money in the bank" calculation, where
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Money in the bank = Guarantee Price x ert
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r = risk-free interest rate
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t = time to maturity
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Thus, the calculated value of the imbedded call was approximately 4.087 points,
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which is an implied volatility of just over 26%. At the time, listed short-term options |