bv_cvxbook_extra_exercises

Here we assume the vector f can take arbitrary values

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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 risk-free 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 risk-return 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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