Learning Outcomes:
On completion of this module the student should be able to:
- implement financial models and techniques in both VBA and Python;
- compute future and present values of a security:
- apply the Binomial Tree Method to price a given option under certain conditions and discuss issues related to the convergence;
- implement the Black-Scholes model;
- price American and Asian options;
- use Monte Carlo methods in option pricing and Greeks estimate;
- use Finite Difference Methods in option pricing;
- price barrier options (time permitting).
Indicative Module Content:
- Derivatives: Forward, Future, Options. Main features and differences.
- A concise introduction to asset pricing: definitions of fair price, trading strategies, self-financing and admissible portfolio. No arbitrage principle, martingales and information. Martingale Measure. Fundamental Theorem of Asset Pricing.
- The Black-Scholes-Merton Model: assumptions, derivation of the BS PDE, uniqueness of solution and equivalence with the heat equation. BS equations for European Call and Put. Greeks. Implied Volatility.
- The binomial model for option pricing: one step tree, replication and risk neutral argument. Multi-Step trees for European and American Options. Exotic Options. The CRR model. Delta-Hedging. Control Variate Technique. Convergence to the BS model.
- Monte Carlo Method: Geometric Brownian Motion generation and risk-neutral valuation. Option Pricing. Greeks Estimation. Antithetic Variate and Control Variate Techniques. Asian Options.
- Finite Difference Method for option pricing: Derivatives approximations and Boundary Conditions. Explicit Method, Implicit Method, Crank-Nicolson Method. Barrier Options.