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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 the risk neutral measure via Girsanov's theorem. D. Self-financing strategy. E. Existence of the 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. Bibliography.

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