39 lines
3.1 KiB
Plaintext
39 lines
3.1 KiB
Plaintext
Chapter 40: Advanced Concepts 849
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Let us now take a look at how both volatility and time affect the delta of a call
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option. Much of the data to be presented in this chapter will be in both tabular and
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graphical form, since some readers prefer one style or the other.
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The volatility of the underlying stock has an effect on delta. If the stock is not
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volatile, then in-the-money options have a higher delta, and out-of-the-money
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options have a lower delta. Figure 40-1 and Table 40-1 depict the deltas of various
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calls on two stocks with differing volatilities. The deltas are shown for various strike
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prices, with the time remaining to expiration equal to 3 months and the underlying
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stock at a price of 50 in all cases. Note that the graph confirms the fact that a low
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volatility stock's in-the-money options have the higher delta. The opposite holds true
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for out-of-the-money options: The high-volatility stock's options have the higher delta
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in that case. Another way to view this data is that a higher-volatility stock's options will
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always have more time value premium than the low-volatility stock's. In-the-money,
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these options with more time value will not track the underlying stock price move
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ment as closely as ones with little or no time value. Thus, in-the-money, the low
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volatility stock's options have the higher delta, since they track the underlying stock
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price movements more closely. Out-of-the-money, the entire price of the option is
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composed of time value premium. The ones with higher time value (the ones on the
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high-volatility stock) will move more since they have a higher price. Thus, out-of-the
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money, the higher-volatility stock's options have the greater delta.
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Time also affects delta. Figures 40-2 (see Table 40-2) and 40-4 show the rela
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tionships between time and delta. Figure 40-2's scales are similar to those in Figure
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40-2, delta vs. volatility: The deltas are shown for various striking prices, with XYZ
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assumed to be equal to 50 in all cases. Notice that in-the-money, the shorter-term
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options have the higher delta. Again, this is because they have the least time value
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premium. Out-of-the-money, the opposite is true: The longer-term options have the
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higher deltas, since these options have the most time value premium.
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Figure 40-3 (see Table 40-3) depicts the delta for an XYZ January 50 call with
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XYZ equal to 50. The horizontal axis in this graph is "weeks until expiration." Note
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that the delta of a longer-term at-the-money option is larger than that of a shorter
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term option. In fact, the delta shrinks more rapidly as expiration draws nearer. Thus,
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even if a stock remains unchanged and its volatility is constant, the delta of its options
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will be altered as time passes. This is an important point to note for the strategist,
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since he is constantly monitoring the risk characteristics of his position. He cannot
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assume that his position is the same just because the stock has remained at the same
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price for a period of time.
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Position Delta. Another usage of the term delta is what has previously been
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referred to as the equivalent stock position (ESP); for futures options, it would be |