Add training workflow, datasets, and runbook
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648 Part V: Index Options and Futures
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Example: The following prices exist:
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ZYX Cash Index: 17 4.49
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ZYX December future: 177.00
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There are 80 days remaining until expiration, the volatility of ZYX is 15%, and
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the risk-free interest rate is 6%.
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In order to evaluate the theoretical value of a ZYX December 185 call, the fol
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lowing steps would be taken:
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l. Evaluate the regular Black-Scholes model using 185 as the strike, 177.00 as the
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stock price, 15% as the volatility, 0.22 as the time remaining (80/365), and 0% as
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the interest rate. Note that the futures price, not the index price, is input to the
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model as stock price.
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Suppose that this yields a result of 2.05.
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2. Discount the result from step l:
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Black Model call value = e-(.0 6 x 0-22) x 2.05
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= 2.02
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In this case, the difference between the Black model and the Black-Scholes
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model is small (3 cents). However, the discounting factor can be large for longer-term
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or deeply in-the-money options.
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The other items of a mathematical nature that were discussed in Chapter 28 on
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mathematical applications are applicable, without change, to index options. Expected
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return and implied volatility have the same meaning. Implied volatility can be calcu
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lated by using the Black-Scholes formulas as specified above.
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Neutral positioning retains its meaning as well. Recall that any of the above the
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oretical value computations gives the delta of the option as a by-product. These deltas
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can be used for cash-based and futures options just as they are used for stock options
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to maintain a neutral position. This is done, of course, by calculating the equivalent
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stock position (or equivalent "index" or "futures" position, in these cases).
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FOLLOW-UP ACTION
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The various types of follow-up action that were applicable to stock options are avail
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able for index options as well. In fact, when one has spread options on the same
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underlying index, these actions are virtually the same. However, when one is doing
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inter-index spreads, there is another type of follow-up picture that is useful. The rea-
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