To provide an understanding of basic theories in Financial Mathematics used in the study process of actuarial/financial interest.

To provide an introduction to financial methods and derivative pricing financial instruments in discrete time set up.

To prepare the students adequately and to develop their skills in order to be ready to sit the CM2 subject of the Institute and Faculty of Actuaries exams.

(LO1) Know how to optimise portfolios and calculating risks associated with investment.

(LO2) Demonstrate principles of markets.

(LO3) Assess risks and rewards of financial products.

(LO4) Understand mathematical principles used for describing financial markets.

(a) Theories of financial market behaviour:

Rational expectations theory, rational choice theory and behavioural economics.

(b) Modern portfolio theory:

Introducing the Capital Asset Pricing Model and its uses, introducing the capital market line and security market line, introducing and deriving the formula for the Arbitrage Pricing Theory model.

(c) Measures of risk:

Measures of investment risk (downside semi-variance of return, shortfall probabilities, VaR, Tail VaR), concepts of moral hazard
and adverse selection in the insurance companies context.

(d) Introduction to markets and options:

Introduction to the concept of forward contracts, over‐the counter and exchange‐traded derivatives, hedging. Options: basics, strategies and profit diagrams, European and American options, put‐call parity, Arbitrage.

(e) Concepts of discrete time stochastic processes:

Concept of Stopping times, Conditional expectatio n in discrete time, discrete time martingales.

(f) Applications of Martingales to Discrete Time Finance:

The concept of arbitrage-free pricing (cash‐and‐carry pricing) will be explained and developed into the fundamental theory of asset pricing in discrete time. Moreover, the module will include the fundamental properties of option prices, risk‐neutral probability measure and incomplete markets, pricing European‐style derivative contracts using binary trees and the binomial model, American options using the binomial model, random walk of asset pricing.