F71AP - Advanced Derivative Pricing

Course leader(s):

Abdul-Lateef Haji-Ali (Edinburgh, January)
To be announced (Dubai, January)

Aims

The aims of this course are:

To provide a thorough grounding in advanced topics of derivative markets
To introduce mathematical concepts related continuous time martingales processes
To provide students with a good understanding of developing the BSM model to different asset price models, including dividends and stochastic volatility
To provide students with a good understanding of pricing American options
To provide students with a good understanding of exotic options
To introduce the student to numerical methods for pricing
To provide students with a good understanding of modelling( the term structure of) interest rates
To introduce the student to securitisation and credit derivatives

Syllabus

1. Stochastic Calculus applied to financial markets (1.1 Ito calculus, Ito’s formula, statement of the Cameron-Martin-Girsanov Theorem, the concept of the Radon-Nikodym derivative, the Martingale Representation Theorem, 1.2 Description of exotic options including Quanto, Chooser, Barrier, Binary, Lookback Asian, Exchange, Basket options, 1.3 Management of derivative portfolios of using scenario analysis., 1.4 Risk management characteristics of certain exotic products, 1.5 Self-financing portfolios in continuous time and the construction of replicating strategies using the martingale approach, 1.6 OU and Feller processes and derivation of BSM PDE, 1.7 The role of the market price of risk in the transfer between the real-world and the risk-neutral probability measures, 1.8 Hedging derivatives and the Greeks in continuous time models and to structures)

2. Volatility (2.1 The role of the volatility parameter in the valuation of options, 2.2 Estimation of volatility from market data, 2.3 The “smile” effect and volatility surfaces)

3. Modelling the Term Structure of Interest Rates (3.1 The Black, Hull & White Vasicek and Cox-Ingersoll-Ross models Ho & Lee, Black, Derman & Toy, Black & Karasinski, 3.2 HJM framework., 3.3 Libor Market Models, 3.4 Implementation and calibration of models)

4. Structured Derivatives and Synthetic Securities (4.1 Products for hedging non-financial risks, 4.2 Securitisation, 4.3 Credit risk, 4.4 CDOs and CDSs)

5. Numerical methods (5.1 Finite differences and lattices, 5.2 Trinomial trees, 5.3 Monte Carlo techniques, 5.4 Least-Squares Longstaff-Schwartz approach for Ameican options)

Learning outcomes

By the end of the course, students should be able to do the following:

appraise mathematical models in finance to identify inherent risks.
explain the process of securitisation including the benefits to different parties and techniques of risk transformation.
explain the mathematical basis of Black-Scholes-Merton formulae and the Fundamental Theorem of Asset Pricing including the significance of the Radon-Nikodym derivative, CMG theorem, and Martingales.
formulate hedging strategies for derivatives and portfolios by utilising the Greeks
explain the significance of volatility in derivatives markets including implied volatility, volatility smiles and the estimation of volatility.
apply Blacks model to pricing options on futures, caps and floors and swaptions and be aware of shortcomings in the approach.
describe the short rate models, HJM and LIBOR Market Model approaches including their motivation and assumptions.
appraise different risk measurement and risk management techniques including Value at Risk and the Gaussian Copula.

Further details

Curriculum explorer: Click here

SCQF Level: 11

Credits: 15