NSCPHD1230 Hedging and Market Consistent Valuation in Life Insurance

Volume 2013/2014
Education
MSc programme in Actuarial Mathematics
Content
On the course we consider valuation of liabilites for life insurance companies and Solvency II capital requirements. There will also be some focus on implementing the methods in practice through numerically solving differential equations and simulation.
In the first part of the course, we consider hedging in complete and incomplete markets of payments associated with a life insurance contract, and how this leads to market values.
In the second part of the course we consider modelling of policyholder behaviour with deterministic surrender and free-policy rates.
In the third part, we consider stochastic interest and transition rates, and see how we can valuate and hedge life insurance liabilities. We also see how these methods can enhance policyholder modelling.
Learning Outcome
1 Knowledge
- Decide when a market is complete or incomplete.
- Explain the concepts of static and dynamic hedging.
- Explain the principle of market values.
- Identify the FS decomposition and use this to find risk-minimising static and dynamic strategies.
- Find market values including surrender and free policy modelling using Markov chain models.
- Explain the basic principle behind the risk measured in the Solvency II rules.
- Identify the Solvency II capital requirement for a risk, and simplifications of the problem.
- Find transition probabilities, market values and Solvency II capital requirements using stochastic interest and transition rates.
- Solve systems of differential equations using Runge-Kutta 2nd and 4th order methods
- Simulation of multidimensional diffusion processes.

2 Skills
- Derive risk-minimising static and dynamic hedging strategies.
- Derive formulas for market consistent values with and without different types of policyholder behaviour modelling.
- Use stochastic transition rates for valuation of life insurance liabilites.
- Numerically solve systems of differential equations for application in life insurance problems.
3 Competences
- Decide optimal static and dynamic hedging strategies.
- Decide, using tools from financial mathematics, when there exists a market value.
- Calculate market consistent values for life insurance contracts using appropriate methods.
- Discuss and assess the qualitative and quantitave impact of different types of policyholder behaviour modelling.
- Calculate and assess Solvency II capital requirements for life insurance contracts.
Liv1, LivStok, FinKont, Liv2 or similar.
4 hours of lectures and 2 hours of exercise sessions per week for 7 weeks.
  • Category
  • Hours
  • Course Preparation
  • 164
  • Lectures
  • 28
  • Theory exercises
  • 14
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Written assignment
Oral examination, 20 minutter
One hand-in exercise during the course. Oral examn, 20 minutes, no preparation. Grade is given based on an overall evaluation of both the hand-in exercise and the oral examination.
Exam registration requirements
Hand-in exercise must be passed.
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner for the written assignment and several internal examiners for the oral exam
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.