Financial Markets II (Exercises from Michal Pakos' CERGE-EI Financial Markets class in Spring 2011)

Risk-neutral valuation in two- and N-period models, State prices, change of measure, Radon-Nikodym process, American derivative securities, optional sampling theorem, Random walk, first passage times, reflection principle, Interest-rate dependent assets – bonds, futures, forwards, swaps; Arbitrage Theory in Continuous Time; Brownian motion (definition, quadratic variation, Markov property, first-passage times, reflection principle, Levy characterization theorem), Stochastic calculus (Ito stochastic integral, multivariate Ito-Doeblin formula, martingale representation theorem, Girsanov theorem, Brownian bridge); Risk-neutral pricing, first and second fundamental theorems of asset pricing, Stochastic differential equations, Feynman-Kac connection to partial differential equations; Change of numeraire, forward measure; Term structure models (affine yield models, Heath-Jarrow-Morton).

References:

Cochrane, John (2005). Asset Pricing. Princeton University Press; Revised Edition edition (January 23, 2005).

Shreve, S. (2005). Stochastic Calculus for Finance I: The Binomial Asset Pricing Model. Springer; 2004 edition (July 29, 2005).

Shreve, S. (2005). Stochastic Calculus for Finance II: Continous Time Models. Springer; 2004 edition (July 29, 2005).

George Pennacchi, Theory of Asset Pricing.