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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.
a. An economy with one risky asset.
b. An economy with two risky assets.
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.

Existence of risk neutral measure via backward Kolmogorov's equation. Delta hedging.


e consider an economy with deterministic riskless rate. Consideration of stochastic riskless rate requires the notion of $T$ -forward probability measure. We postpone such consideration until the notion is developed.




a. An economy with one risky asset.
b. An economy with two risky assets.

Notation. Index. Contents.


















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