Module Catalogues, Xi'an Jiaotong-Liverpool University   
Module Code: MTH312
Module Title: Stochastic Modeling in Insurance and Finance
Module Level: Level 3
Module Credits: 5.00
Academic Year: 2019/20
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: N/A
This module introduces various stochastic models for different actuarial and financial problems. The aim of this module is to develop the necessary skills to construct asset liabilities models and to value financial derivatives. The students are required to understand the developments of quantitative models to solve practical problems. The module helps students write actuarial professional exam.

Learning outcomes 
A. Understand the continuous time log-normal model of security prices, auto-regressive model of security prices and other economic variables (e.g. Wilkie model). Define and apply the main concepts of standard Brownian motion and geometric Brownian motion.

B. Understand the properties of risk-neutral measure in valuing option.

C. Explain how to price and hedge simple derivative contracts using the martingale approach. Be aware of the first and second partial derivative (Greeks) of an option price.

D. Price zero-coupon bonds and interest–rate derivatives for a general one-factor diffusion model for the risk-free rate of interest via both risk-neutral and state-price deflator approach. Understand the limitations of the one-factor models

E. Demonstrate a knowledge and understanding of simple models for credit risk and understand the two-state model for the credit ratings

F. Understand, construct and apply asset and liability valuations models.

G. Understand and explain the theories on the behaviour of financial markets.
Method of teaching and learning 
This module is delivered through formal lectures and tutorial classes
* Measures of risk

Variance of return, downside sime-variance of return, shortfall probabilities, Value at Risk (VaR), Tail VaR; perform calculation using risk measures and explain how the distribution of returns and the thickness of tails will influence the assessment of risk.

• Stochastic modelling of the behaviour of the security prices

Continuous time log-normal model of security prices, auto-regressive models of security prices and other economic variables (e.g. Wilkie model): discussion, simple calculations involving the models, comparison with alternative models, advantages and disadvantages.

• Ito Formula: theory and applications

Standard Brownian motion, Ito integral, mean-reverting processes: definition and basic properties. Ito’s formula: statement and application in simple problems. Stochastic differential equations for geometric Brownian motion and Ornstein-Uhlenbeck process: derivation of solutions.

• Options pricing, valuation and hedging

Arbitrage, complete markets and factors influencing the option prices. Specific results: valuation of a forward contract; upper and lower bounds for European and American call and put options.

• Martingale measures and derivative pricing model

Complete market, risk-neutral pricing and equivalent martingale measure, price and hedge simple derivative contracts using the martingale approach. Black–Scholes partial differential equation. Pricing via state-price deflators: apply in simple models as binomial model and Black-Scholes model and demonstrate equivalence to risk-neutral pricing. Partial derivatives (Greeks) of an option price: first and second derivative.

• Models for the term-structure of interest rates

Models for the term structure interest rates: desirable characteristics; Vasicek, Cox-Ingersoll-Ross and Hull-White models. Pricing zero-coupon bonds and interest–rate derivatives for a general one-factor diffusion model for the risk-free rate of interest: risk-neutral approach versus state-price deflator approach.

• Portfolio theory

Mean-variance portfolio theory; Capital Asset Pricing Model (CAPM); Single and multifactor models for investment returns.

• Liability valuations

Ruin theory: aggregate claim process and the cash-flow process; Run-off triangles: development factor; chain ladder method; average cost per claim method; Bornhuetter-Ferguson method;

• Theories of financial market behaviour

Rational choice theory: utility function; utility theory; economic properties of common utility functions; dominance; associated insurance problems. Behavioural economics: Kahneman and Tversky’s prospect theory; Bernartzi and Thaler solution

Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 39    13      98  150 


Sequence Method % of Final Mark
1 Assignments 15.00
2 Midterm Exam 15.00
3 Final Exam 70.00

Module Catalogue generated from SITS CUT-OFF: 8/20/2019 6:25:15 PM