16 lines
1.1 KiB
Plaintext
16 lines
1.1 KiB
Plaintext
Cl,apter 33: Mathematical Considerations for Index Products 651
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The astute reader will notice that the above example can be generalized by
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drawing a three-dimensional graph. The X axis would be the price of ZYX; the Y axis
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would be the dollars of profit in the spread; and instead of "sliding scales," the Z axis
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would be the price of ABX. There is software that can draw 3-dimensional profit
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graphs, although they are somewhat difficult to read. The previous tables would then
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be horizontal planes of the three-dimensional graph.
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This concludes the chapter on riskless arbitrage and mathematical modeling.
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Recall that arbitrage in stock options can affect stock prices. The arbitrage
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techniques outlined here do not affect the indices themselves. That is done by the
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market basket hedges. It was also known that no new models are necessary for
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evaluation. For index options, one merely has to properly evaluate the dividend for
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usage in the standard Black-Scholes model. Future options can be evaluated by set
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ting the risk-free interest rate to 0% in the Black-Scholes model and discounting the
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result, which is the Black model.
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