Aviva 2009 Annual Report Download - page 311

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Performance review
Aviva plc MCEV financial statements continued
Corporate responsibility
Annual Report and Accounts 2009
Governance
Shareholder information
Financial statements IFRS
Financial statements MCEV
Other information
M18 – Principal economic assumptions continued
Model – United Kingdom, Europe (excluding Delta Lloyd) and North America
Swap rates are generated by a model, the LIBOR Market Model (LMM), that projects a full swap curve at monthly intervals.
Forward rates are assumed to have a log-normal distribution which guarantees non-negative interest rates. The model is calibrated
to at-the-money swaptions of a variety of terms and tenors. Swaption volatilities are taken from Bloomberg. Tests have been
performed to ensure that sufficient scenarios have been used that the result converges to the stochastic value of the business
being valued.
The total annual return on equities is calculated as the return on one-year swaps plus an excess return. This excess return is
modelled using a log-normal model where volatility varies by time horizon. This allows the model to capture the term structure of
implied volatilities. The model is calibrated to at-the-money options of a variety of terms. Option volatilities are taken from a survey
of investment banks.
The model also generates property total returns and real yield curves, although these are not significant asset classes for Aviva
outside the UK. In the absence of liquid market data, the volatilities of these asset classes are based on historic data.
Assumptions for correlations between asset classes have been set based on historic data.
Model – Delta Lloyd
In Delta Lloyd, yield curves are based on De Nederlandsche Bank (DNB) yield curve data.
The interest rate model used is a short rate G2++ model. The model is calibrated to the DNB yield curve and the swaption
implied volatilities. Swaption implied volatilities are taken from Bloomberg. The equity model is a Heston model.
Asset classes
The significant asset classes for UK participating business are equities, property and long-term fixed rate bonds. The most
significant assumption is the distribution of future long-term interest rates, since this is the most important factor in the cost
of guaranteed annuity options.
For many businesses, including US, France and Delta Lloyd, the most important assets are fixed rate bonds of various
durations.
Summary statistics
Swaption implied volatilities
The implied volatility is that determined by Black-Scholes’ formula to reproduce the market price of the option. The following table
sets out the model swaption implied volatilities.
2009 Swap length 2008 Swap length
Option length 10 years 15 years 20 years 25 years 10 years 15 years 20 years 25 years
UK sterling
10 years n/a n/a 14.1% n/a n/a n/a 11.8% n/a
15 years n/a n/a 14.6% n/a n/a n/a 11.9% n/a
20 years n/a n/a 14.4% n/a n/a n/a 12.1% n/a
25 years n/a n/a 14.0% n/a n/a n/a 12.4% n/a
Euro
10 years 17.9% 17.8% 17.7% 17.6% 11.7% 11.7% 11.7% 11.8%
15 years 18.0% 17.6% 17.3% 16.9% 10.9% 10.9% 10.4% 10.9%
20 years 17.1% 16.7% 16.3% 15.7% 10.5% 10.4% 10.4% 10.3%
25 years 16.2% 15.6% 15.0% 14.4% 10.0% 10.0% 9.9% 9.5%
Delta Lloyd
10 years 14.5% 15.3% 17.3% 18.6% 11.6% 11.6% 11.7% 11.7%
15 years 15.2% 15.8% 17.8% 18.9% 10.8% 10.7% 10.6% 10.8%
20 years 15.8% 16.7% 18.1% 18.5% 10.5% 10.3% 10.2% 10.3%
25 years 16.8% 17.5% 18.2% 18.3% 10.0% 9.8% 9.8% 9.7%
US dollar
10 years 20.0% 18.9% 18.0% 17.3% 15.2% 14.4% 14.0% 14.0%
15 years 17.5% 16.4% 15.6% 15.0% 13.9% 13.0% 12.8% 12.7%
20 years 15.5% 14.5% 13.8% 13.2% 13.3% 12.4% 12.1% 12.1%
25 years 13.7% 12.9% 12.2% 11.6% 12.9% 11.9% 11.6% 11.7%
For businesses, where stochastic scenarios are calibrated before the year end, the closing embedded value has been adjusted for the subsequent decrease in market volatilities up to the year end.
Equity implied volatilities
The implied volatility is that determined by the Black-Scholes’ formula to reproduce the market price of the option. The following
tables set out the model equity implied volatilities.
2009 2008
Option length UK France Italy Ireland
Delta
Lloyd Spain US UK France Italy Ireland
Delta
Lloyd Spain US
5 years
10 years
15 years
25.3%
26.6%
27.3%
29.2%
29.0%
30.0%
26.9%
26.5%
26.4%
27.7%
27.3%
28.1%
27.5%
29.1%
30.5%
27.0%
25.7%
26.5%
26.9%
27.8%
29.1%
25.8%
27.2%
27.7%
24.9%
26.3%
n/a
24.4%
n/a
n/a
24.5%
26.2%
27.0%
26.1%
26.8%
27.1%
26.3%
28.8%
n/a
24.6%
27.3%
28.9%
Financial statements MCEV