Derivative Mathematics
Learn the essential mathematics used in the valuation and risk management of derivatives in an intuitive, accessible fashion. Develop deep insights into concepts such as complete markets, stochastic processes, Ito's lemma and the replication principle.
CPE Credits: 14
This course is a component of the Advanced Derivatives Professional Certificate.
Prerequisite knowledge:
- Familiarity with derivative instruments
- Intermediate to advanced MS Excel skills
- Intermediate probability and statistics
- Basic calculus, including partial differentiation and integration
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To make it even easier to learn, you can finance your program through Affirm.
Loans offered through Affirm are available in the U.S. and Canada.
Module 1: Review of Derivatives Basics
- The no-arbitrage pricing principle
- Objective vs. risk-neutral probabilities
- Forwards and Futures
- Swaps
- Options
- Put-Call Parity
Module 2: Discrete Processes for Asset Prices
- Discrete stochastic processes
- The Markov property
- The Martingale property
- Quadratic variation
- The binomial model
- The trinomial model
Module 3: Discrete Time and State Pricing Models for Derivatives
- A binomial formula for European options
- American options
- Options on assets paying dividends
- Options on stock indices, bonds, currencies, futures and commodities
Module 1: Continuous Processes for Asset Prices
- The Wiener process as the limit of a random walk
- Brownian motion and Ito processes
- Basic stochastic integration
- Functions of stochastic processes
- Ito's lemma
- Jump-diffusion processes
Module 2: Continuous Time and State Pricing Models for Derivatives
- No-arbitrage in continuous time
- The Black-Scholes-Merton partial differential equation
- Black-Scholes-Merton formulas for options
- The Greeks
- American options in continuous time
Module 3: Volatility
- Historical vs Implied Volatility
- Estimating volatility
- Implied volatility surfaces: Skews and smiles
- GARCH models
- Stochastic volatility