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Quantitative Analysis
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I. Basic math.
II. Pricing and Hedging.
1. Basics of derivative pricing I.
2. Change of numeraire.
3. Basics of derivative pricing II.
4. Market model.
5. Currency Exchange.
6. Credit risk.
7. Incomplete markets.
A. Single time period discrete price incomplete market.
B. Coherent measure.
C. Incomplete market with multiple participants.
D. Example: uncertain local volatility.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Incomplete markets.


e review several points of view on pricing, hedging and making decisions in incomplete markets. We start from brief summary of what we want from a good model of incomplete market.

By the assumption of incompleteness we cannot hedge and/or replicate perfectly. Hence, we would like to develop a recipe for identification of good investment opportunities. Hopefully, such a recipe should be stated in terms of a "price" of personal nature, depending on portfolio, risk preference, credit rating and so fourth. The following are some of the desirable features.

1. The model should include all observable quantitative data. In particular, we do not want to discard historical information.

2. The model should be dynamic. We want to hedge and may want to exit the position early. Consequently, the liquidity information should be included.

3. The model should deliver inventory control. It should not recommend taking unlimited exposure when a good opportunity is discovered. Hence, the attractiveness of an investment decision should vanish as we accumulate exposure in line with such investment decision. Consequently, current position should be a part of the model.

4. The set of "good" opportunities should include those leading to possible losses. We may take risk if the somehow evaluated potential gain makes the investment attractive.

5. Absence of "good" opportunities for all market participants should cause existence of generally accepted pricing.

6. All sources of incompleteness (lack of liquidity, transaction costs, trading restrictions, unheadgeable risks...) should increase bid/ask spread. Willingness to take risk should decrease bid/ask spread.




A. Single time period discrete price incomplete market.
B. Coherent measure.
C. Incomplete market with multiple participants.
D. Example: uncertain local volatility.

Notation. Index. Contents.


















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