1. Extensions of the Black-Scholes model: Dividends, currency derivatives.
2. Incomplete markets: Pricing in a factor model, the market price of risk.
3. The martingale approach to arbitrage pricing. Martingale measures. The first and second fundamental theorems.
4. Interest rate theory: Short rate models, affine term structures, inversion of the yield curve, forward rate models, the HJM approach.
5. Change of numeraire: The normalized economy, pricing in a new numeraire, forward measures, the general option pricing formula, forward and futures contracts.
6. LIBOR and swaption market models.
The objective of the course is to present the fundamentals of arbitrage theory for pricing contingent claims in continuous time.
Whiteboard, open discussions, presentations by students. Lecture notes are available.
Grades are based on the (quality of) solution of exercises, presentations, and a final written test.
More precisely the students are assumed to have basic knowledge of the following mathematical areas:
• Measure and integration theory, including the Radon Nikodym theorem
• Stochastic differential equations
• The Kolmogorov backward equation
• The Feynman-Kac representation Theorem• The Ito formula
• The Girsanov Theorem
• The stochastic integral representation Theorem for Wiener martingalesThe students are also assumed to be familiar with elementary theory for arbitrage free pricing and hedging of European derivatives within the Black-Scholes model.
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