Description
Aims:
This module introduces the applied mathematical and computational aspects of Quantitative Finance.
Intended learning outcomes:
On successful completion of the module, a student will be able to:
- Apply the necessary probability and differential equation-based approach to the pricing of financial derivatives, using both quantitative and numerical techniques.
Indicative content:
The following are indicative of the topics the module will typically cover:
Financial Products and Markets:
- Time value of money and applications. Equities, indices, foreign exchange, and commodities. Futures, Forwards and Options. Payoff, and P&L diagrams. Put-Call parity. The Binomial model and risk-neutrality.
Stochastic Calculus:
- Brownian motion and properties, Itô’s lemma and Itô integral. Stochastic Differential Equations – drift and diffusion; Geometric Brownian Motion and Vasicek model.
- Forward and Backward Kolmogorov equations for the transition density.
- Random number generation in Excel – RAND(), NORMSINV(), simulating random walks, correlations. Examining statistical properties of stock returns.
Black-Scholes Model:
- Assumptions, PDE and pricing formulae for European calls and puts. Extending to dividends, FX and commodities.
- The Greeks and risk management - theta, delta, gamma, vega, rho and their role in hedging. Two factor models and multi-asset options; Mathematics of early exercise:
- Computational Finance: Solving the pricing PDEs numerically using the Finite Difference Scheme. The Monte-Carlo method.
Fixed-Income world:
- Zero coupon bonds and coupon bearing bonds; yield curves, duration and convexity. Bond Pricing Equation (BPE). Popular models for the spot rate.
- Stochastic interest rate models - Vasicek, CIR, Ho and Lee, and Hull and White.
- Solutions of the BPE.
Introduction to Exotics:
- Basic features and classification of exotic options. Weak and strong path dependency
- Barriers, Asians and Lookbacks. Sampling continuous and discrete.
- Pricing using the PDE framework.
Requisites:
To be eligible to select this module as optional or elective, a student must: (1) be registered on a programme and year of study for which it is a formally available; (2) have a good understanding of basic probability and differential equations.
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 19th August 2024.
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