Add training workflow, datasets, and runbook
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Chapter 40: Advanced Concepts
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p2 = p 1 +delta+ gamma, or substituting from above
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p2 = (p0 + delta) + delta + gamma
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= Po + 2 x delta + gamma
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6.04 = 5.00 + 2 x 0.505 + 0.03 (in the example if XYZ = 90)
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875
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By the same calculation, the put in the example will be priced at 4.04 if XYZ imme
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diately jumps to 90:
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4.04 = 5.00 - 2 X 0.495 + 0.03
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So, overall, the call will have increased by 1.04, but the put will only have
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decreased by 0.96. The unrealized loss would then be computed as -$10,400 for the
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100 calls, offset by a gain of $9,600 on the sale of 100 puts, for a net unrealized loss
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of $800. This verifies the result obtained above using position delta and position
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gamma. Again, this confirms the logical fact that a quick stock movement will cause
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unrealized losses in a short straddle position.
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Continuing on, let us look at some of the other factors affecting the sale of this
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straddle. The straddle seller has time working in his favor. After the position is estab
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lished, there will not be as much decay in the first two-week period as there will be
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when expiration draws near. The exact amount of time decay to expect can be calcu
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lated from the theta of the position:
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XYZ: 88
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Position
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Sold l 00 July 90 calls
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Sold l 00 July 90 puts
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Option
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Theta
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-0.03
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-0.03
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Position
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Theta
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+$300
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+$300
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+$600
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This is how the position looked with respect to time decay when it was first
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established (XYZ at 88 and three months remaining until expiration). The theta of the
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put and the call are essentially the same, and indicate that each option is losing about
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3 cents of value each day. Note that the theta is expressed as a negative number, and
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since these options are sold, the position theta is a positive number. A positive posi
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tion theta means time decay is working in your favor. One could expect to make $300
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per day from the sale of the 100 calls. He could expect to make another $300 per day
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from the sale of the 100 puts. Thus, his overall position is generating a theoretical
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profit from time decay of $600 per day.
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The fact that the sale of a straddle generates profits from time decay is not
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earth-shattering. That is a well-known fact. However, the amount of that time decay
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