 to provide an understanding of the basic financial mathematics theory used in the study process of actuarial/financial interest,

 to provide an introduction to financial methods and derivative pricing financial instruments ,

 to understand some financial models with applications to financial/insurance industry,

 to prepare the students adequately and to develop their skills in order to be ready to sit for the CT1 & CT8 subject of the Institute of Actuaries (covers 20% of CT1 and material of CT8).

After completing the module students should:

(a) Understand the assumptions of CAMP, explain the no riskless lending or borrowing and other lending and borrowing assumptions, be able to use the formulas of CAMP, be able to derive the capital market line and security market line,

(b) Describe the Arbitrage Theory Model (APT) and explain its assumptions, perform estimating and testing in APT,

(c) Be able to explain the terms long/short position, spot/delivery/forward price, understand the use of future contracts, describe what a call/put option (European/American) is and be able to makes graphs and explain their payouts, describe the hedging for reducing the exposure to risk, be able to explain arbitrage, understand the mechanism of short sales,

(d) Explain/describe what arbitrage is, and also the risk neutral probability measure, explain/describe and be able to use (perform calculation) the binomial tree for European and American style options,

(e) Understand the probabilistic interpretation and the basic concept of the random walk of asset pricing,

(f) Understand the concepts of replication, hedging, and delta hedging in continuous time,

(g) Be able to use Ito''s formula, derive/use the the Black‐Scholes formula, price contingent claims (in particular European/American style options and forward contracts), be able to explain the properties of the Black‐Scholes formula, be able to use the Normal distribution function in numerical examples of pricing,

(h) Understand the role of Greeks , describe intuitively what Delta, Theta , Gamma is, and be able to calculate them in numerical examples.

(a) Modern portfolio theory
Introduce the Capital Asset Pricing Model and the uses of the CAMP, the capital market line and security market line, introduce and derive the formula for the Arbitrage Pricing Theory model.

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

(c) Discrete time Finance
The concept of arbitrage free pricing (cash‐and‐carry pricing) will be explained and developed into the fundamental theorem of asset pricing in discrete time, the fundamental properties of option prices, no‐arbitrage pricing, the risk‐neutral probability measure and incomplete markets, pricing European‐style derivative contracts using bi nary trees and the binomial model, American options using the binomial model, random walk of asset pricing, the binomial model for stock prices and the Cox‐Ross‐Rubensein model.

(d) Continuous time finance
Introduction to the concept of diffusion equations and their boundary conditions, the Brownian motion and its properties, calibration of the Binomial model as an approximation to Brownian motion, the Ito''s formula (for pricing options), the Black‐Scholes formula, extend the Black‐Scholes formula to foreign currencies and dividend paying stocks, introduce the Greeks in portfolio risk management (Delta hedging, Delta of European stock options, Theta -- time decay of the portfolio, the Gamma).