CHAPTER 33 
Mathetnatical Considerations 
for Index Products 
In this chapter, we look at some riskless arbitrage techniques as they apply to index 
options. Then a summary of mathematical techniques, especially modeling, is pre­
sented. 
ARBITRAGE 
Most of the normal arbitrage strategies have been described previously. We will 
review them here, concentrating on specific techniques not described in previous 
chapters on hedging (market baskets) and index spreading. 
DISCOUNTING 
We saw that discounting in cash-based options is done with in-the-money options as 
it is with stock options. However, since the discounter cannot exactly hedge the cash­
based options, he will normally do his discounting near the close of the day so that 
there is as little time as possible between the time the option is bought and the close 
of the market. This reduces the risk that the underlying index can move too far before 
the close of trading. 
Example: OEX is trading at 673.53 7nd an arbitrageur can buy the June 690 puts for 
16. That is a discount of 0.47 since,parity is 16.47. Is this enough of a discount? That 
is, can the discounter buy this put, hold it unhedged until the close of trading, and 
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