Intended Schedule
Note that the lecture numbers and contents can change without notice.
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Money: The Zero Coupon Bond.
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Bond portfolios and immunization.
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Instruments: Stocks, Derivatives (mainly Options).
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Prediction and Trading.
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Measures of trading performance. Ex-post optimal trading
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Arbitrage and the Martingale Measure.
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Proof of the positive supporting price theorem.
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The risk neutral world and expectations.
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Binomial models for geometric Brownian stock dynamics.
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Pricing using Martingale measures in binomial models.
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Monte Carlo methods for pricing almost arbitrary derivatives.
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Path Generation in Monte Carlo Methods.
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Introduction to Monte Carlo.
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Variance reduction
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Importance sampling and low discrepancy sequences.
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Analytic pricing: The European options; barrier options.
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Stochastic Calculus.
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The PDE approach.
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The American Put option: Dynamic programming on the binomial tree.
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The American Put option: LeastSquaresMethod and OPTimal
for finding the exercise boundary.
Backward path generation, efficiency and memory issues.
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Pricing the American Put by optimizing bounds.
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Estimating and predicting parameters in the stock price dynamics:
Maximum likelihood; Cross Entropy; ARCH and GARCH.
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Portfolio Optimization: mean-variance analysis.
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Portfolio optimization as Mixed Integer Linear Programs (MILPs).
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Value at Risk (VAR) and evaluation of loan portfolios.
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Monte Carlo estimates of rare event probabilities.
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Auctions.
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Distributed ledgers and digital currency -- BitCoin