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Unformatted text preview: option limits both the upside and downside of payoﬀ.
Now we consider a speciﬁc problem. The price of the riskfree asset, with r = 1.05, is 1. The price
of the underlying asset is S0 = 1. We will use m = 200 scenarios, with S (i) uniformly spaced from
S (1) = 0.5 to S (200) = 2. The following options are traded on an exchange, with prices listed below.
Type
Call
Call
Put
Put Strike
1.1
1.2
0.8
0.7 Price
0.06
0.03
0.02
0.01. A collar with ﬂoor F = 0.9 and cap C = 1.15 is not traded on an exchange. Find the range of
prices for this collar, consistent with the absence of arbitrage and the prices given above.
13.17 Portfolio optimization with qualitative return forecasts. We consider the riskreturn portfolio optimization problem described on pages 155 and 185 of the book, with one twist: We don’t precisely
know the mean return vector p. Instead, we have a range of possible values for each asset, i.e., we
¯
n
have l, u ∈ R with l
p
¯ u. We use l and u to encode various qualitative forecasts we ha...
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 Fall '13
 F.Borrelli
 The Aeneid

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