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I. Basic math.
II. Pricing and Hedging.
1. Basics of derivative pricing I.
A. Single step binary tree argument. Risk neutral probability. Delta hedging.
B. Why Ito process?
C. Existence of risk neutral measure via Girsanov's theorem.
D. Self-financing strategy.
E. Existence of risk neutral measure via backward Kolmogorov's equation. Delta hedging.
F. Optimal utility function based interpretation of delta hedging.
2. Change of numeraire.
3. Basics of derivative pricing II.
4. Market model.
5. Currency Exchange.
6. Credit risk.
7. Incomplete markets.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Self-financing strategy.

he argument of the section ( Risk neutral measure via Girsanov section ) has local nature with respect to time. After we advance to the next time moment, the local dW-independence would be lost. Hence, we would need to rebalance the portfolio. The rebalancing condition is called "self-financing" condition:

MATH (Self financing strategy)
We already used it in the previous section. It means that the value of the portfolio changes only because the asset prices change. There is no inflow of money. For this to be generically viable we need to assume that the money market account is among components of $S$ . Once we agree on such restriction, we need to know that we will not run out of money. In other words, we need to know that we can always install the dynamic hedge. Such results are not yet included in these notes.

Notation. Index. Contents.

Copyright 2007