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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. A. Delta hedging in a situation of predictable jump I. B. Delta hedging in a situation of predictable jump II. C. Backward Kolmogorov's equation for a jump diffusion. D. Risk neutral valuation in the predictable jump size situation. E. Examples of credit derivative pricing. F. Credit correlation. G. Valuation of CDO tranches. a. Definitions of CDO contract. b. Present values of CDO tranches. c. Distribution of defaulted notional of CDO tranches. 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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