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(a) Modern portfolio theory Introduce the Capital Asset Pricing Model and the uses of the CAMP, the capital market line and security market line, introduce and derive the formula for the Arbitrage Pricing Theory model. (b) Introduction to markets and options Introduction to the concept of forward contracts, over‐the counter and exchange‐traded derivatives, use in hedging. Options: basics, strategies and profit diagrams, European and American options, put‐call parity. (c) Discrete time Finance The concept of arbitrage free pricing (cash‐and‐carry pricing) will be explained and developed into the fundamental theorem of asset pricing in discrete time, the fundamental properties of option prices, no‐arbitrage pricing, the risk‐neutral probability measure and incomplete markets, pricing European‐style derivative contracts using binary trees and the binomial model, American options using the binomial model, random walk of
asset pricing, the binomial model for stock prices and the Cox‐Ross‐Rubensein model. (d) Continuous time finance Introduction to the concept of diffusion equations and their boundary conditions, the Brownian motion and its properties, calibration of the Binomial model as an approximation to Brownian motion, the Ito's formula (for pricing options), the Black‐Scholes formula, extend the Black‐Scholes formula to foreign currencies and dividend paying stocks, introduce the Greeks in portfolio risk management (Delta hedging, Delta of European stock options, Theta -- time decay of the portfolio, the Gamma).
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