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Lecture 4: Application of Malliavin calculus to exact and approximate option pricing under stochastic volatility

Introduction Model of asset price and payoff function: additional assumptions, auxiliary properties Elements of Malliavin calculus and application to option pricing The rate of convergence of…

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Lectures 27-28: the Girsanov theorem and the martingale representation theorem

Levy's characterization of Brownian motion. Drift transformation in the Brownian motion and the Girsanov theorem. The martingale representation theorem. Representation of densities of…

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Lecture 26: change of probability with a filtration

Equivalent probability measures. Conditional expectation and martingales under the new probability.

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Lecture 24: change of probability

Absolutely continuous probability measures. Measures defined by a density. The Radon-Nykodym theorem. Expectation under the new probability.

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