Financial Engineering

uni zurich spring 2025

“Financial engineering” is about equity derivatives, modeling and pricing. After introducing fundamental concepts of mathematical finance, including no-arbitrage, portfolio replication, and the risk-neutral measure, we will present the main models that can be used for pricing and hedging European options and highlight their assumptions and limitations. We will cover several types of derivatives, such as European options and exotic options.

Contents

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  1. Introduction to Financial Engineering
    1. Introducing the Objects or our Study
    2. Basic Equity Products
    3. No Arbitrage Pricing
    4. Static and Dynamic Replication
  2. The Binomial Model
    1. One-Period Binomial Model
    2. Multiperiod Binomial Model
  3. Brownian Motion
    1. Introduction
    2. Stock Price Dynamics
    3. Random Walk
    4. Three Key Properties
  4. Itô’s Calculus
    1. Differentiation
    2. Integration
    3. Generalization
  5. The Black-Scholes Model
    1. Assumptions
    2. Derivation
    3. Greeks and Hedging
  6. Exotic Options
    1. Gaussian Shift Theorem
    2. Simple Exotic Options
    3. Dual Expiry Options