Fair Valuation of Guaranteed Contracts:

1

• Fair Valuation of Guaranteed Contracts
• the Interaction Between Assets and Liabilities
• Erwin Charlier
• Tilburg University and ABN AMRO Bank
• Joint work with Ruud Kleynen
• Maastricht University and Kleynen Consultants

2
Overview

• Introduction
• General theoretical framework
• Modelling the assets and the short-rate
• Data and parameter estimation
• Results
• Conclusions
• Further research

3
Introduction

• Balance sheet book value accounting ? fair or
  market value of assets and liabilities
• Market value of assets
• Market prices for publicly traded assets (stocks,
  bonds)
• Valuation models for less liquid assets like real
  estate
• Market value of liabilities
• Very little traded liabilities
• Optionalities

4
Introduction

• In this presentation
• Simple insurer
• Assets investments in stocks and bonds
• Liabilities and equity
• Single guaranteed return contract (policy)
• Equity
• Policy characteristics
• Guaranteed return, roffered
• Bonus if the return on equity exceeds roffered
  then fraction of surplus to policyholder

5
General theoretical framework

• t0
• tT

6
General theoretical framework

• 0lttltT
• t0 no cross-subsidizing
• Note prices under risk-neutral measure

7
Modelling the assets and the instantaneous
short-rate

• Instantaneous short-rate stochastic, Vasicek
• LN gross asset returns normal
• Geometric Brownian motions correlated
• Under risk-neutral measure analytic formulae for
  price of put and call
• Real-world measure used to describe economy at
  time t, also input for prices

8
Data and parameter estimation

• Parameters in process for instantaneous
  short-rate
• Cross-section of FR bond prices (Feb 28, 2002)
• Time-series of 1-month FIBOR rates
• Also used to derive instantaneous short-rate
  series
• Parameters in process for assets
• Assume two investment categories stocks and
  bonds (monthly, Nov 1990-Feb 2002)
• Use weights to construct time-series of portfolio
  returns
• But high mean ? used Dimson(2002)
• Correlation use imputed instantaneous short-rate
  and portfolio returns

9
Results
alpha0.95, delta0.91, roffered0.04, T10
10
Results
alpha0.8, delta0.72, roffered0.04, T10
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Conclusions

• Model allows for stochastic interest rates that
  can be correlated with process for assets.
• Parameters in the model estimated from data
  instead of choosing some value.
• Using both risk-neutral and real-world measure we
  can derive risk-return profiles for both
  policyholders and equityholders.
• Different specifications of the debt-equity ratio
  and the contract did not lead to satisfying
  return profiles for both policyholders and
  equityholders.
• Best results for equityholder occur with low
  debt-equity ratios, conflicting practice.

12
Further research

• Further investigate causes of unsatisfactory
  risk-return profiles.
• Extend to more complicated balance sheet (more
  than one product, different maturities for the
  policies, etc.).
• Consider balance sheet at intermediate times with
  rule for regulator to interfere.
• Use more advanced models to describe the
  instantaneous short-rate and the assets, while
  keeping closed-form solutions for the options.
• Drop the requirement of no cross-subsidizing.