37 lines
2.5 KiB
Plaintext
37 lines
2.5 KiB
Plaintext
G,pter 32: Strudured Products 635
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Such discrepancies will be most notable when there is not a listed option that
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has terms near the terms of the PERCS's imbedded call. If there is such a listed
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option, then arbitrageurs should be able to use it and the common stock to bring the
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PERCS into line. However, if there is not any such listed option available, there may
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be opportunities for theoretical value traders.
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Models used for pricing call options, such as the Black-Scholes model, are dis
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cussed in Chapter 28 on mathematical applications. These models can be used to
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value the imbedded call in the PERCS as well. If the strategist determines the
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implied value of the imbedded call is out of line, he may be able to make a profitable
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trade. It is a fairly simple matter to determine the implied value of the imbedded call.
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The formula to be used is:
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Imbedded call implied value = Current stock price
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+ Present value of dividends - Current PERCS price
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The validity of this formula can be seen by referring again to Figure 32-7. The
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difference between the Final Value (that is, the profit of the covered write at expira
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tion) and the Issue Value or current value of the PERCS is the imbedded call price.
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That is, the difference between the curved line and the line at expiration is merely
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the present time value of the imbedded call. Since this formula is describing an out
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of-the-money situation, then the time value of the imbedded call is its entire price.
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It is also known that the Final Value line differs from the current stock price by the
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present value of all the additional dividends to be paid by the PERCS until maturity.
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Thus, the four variables are related by the simple formula given above.
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Example: XYZ has fallen to 32 after the PERCS was issued. The PERCS is current
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ly trading at 34 and, as in previous examples, the PERCS pays an additional $1.50 per
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year in dividends. If there are two years remaining until maturity of the PERCS, what
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is the value of the imbedded call option?
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First, calculate the present value of the additional dividends. One should calcu
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late the present value of each dividend. Since they are paid quarterly, there will be
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eight of them between now and maturity.
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Assume the short-term interest rate is 6%. Each additional quarterly dividend
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is $0.375 ($1.50 divided by 4). Thus, the present value of the dividend to be paid in
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three months is:
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pw = 0.375/(1 + .06)114 = $0.3696
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The present value of the dividend to be paid two years from now is:
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pw = 0.375/(1 + .06)2 = $0.338
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