39 lines
1.8 KiB
Plaintext
39 lines
1.8 KiB
Plaintext
440 Part IV: Additional Considerations
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manner, the conversion is merely the purchase of a (listed) put and the simultaneous
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sale of a (synthetic) put. Many equivalent strategies can be combined for arbitrage
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purposes. One of the more common ones is the box spread.
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Recall that it was shown that a bull spread or a bear spread could be construct
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ed with either puts or calls. Thus, if one were to simultaneously buy a (call) bull
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spread and buy a (put) bear spread, he could have an arbitrage. In essence, he is
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merely buying and selling equivalent spreads. If the price differentials work out cor
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rectly, a risk-free arbitrage may be possible.
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Example: The following prices exist:
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XYZ common, 55
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XYZ January 50 call, 7
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XYZ January 50 put, 1
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XYZ January 60 call, 2
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XYZ January 60 put, 5½
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The arbitrageur could establish the box spread in this example by executing the
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following transactions:
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Buy a call bull spread:
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Buy XYZ January 50 call
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Sell XYZ January 60 call
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Net call cost
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Buy a put bear spread:
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Buy XYZ January 60 put
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Sell XYZ January 50 put
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Net put cost
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Total cost of position
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7 debit
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2 credit
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51/2 debit
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1 credit
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5 debit
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No matter where XYZ is at January expiration, this position will be worth 10 points.
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The arbitrageur has locked in a risk-free profit of½ point, since he "bought" the box
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spread for 9½ points and will be able to "sell" it for 10 points at expiration. To verify
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this, evaluate the position at expiration, first with XYZ above 60, then with XYZ
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between 50 and 60, and finally with XYZ below 50. If XYZ is above 60 at expiration,
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the puts will expire worthless and the call bull spread will be at its maximum poten
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tial of 10 points, the difference between the striking prices. Thus, the position can be
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liquidated for 10 points if XYZ is above 60 at expiration. Now assume that XYZ is |