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BANCO BILBAO VIZCAYA ARGENTARIA, S.A. AND ... - BBVA

BANCO BILBAO VIZCAYA ARGENTARIA, S.A. AND ... - BBVA

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Financial Instruments<br />

LEVEL 3<br />

Valuation techniques<br />

Main assumptions<br />

Main<br />

unobservable<br />

inputs<br />

JUNE 2010<br />

Fair Value (Millions of Euros)<br />

• Debt securities<br />

• Present-value method; and<br />

• “Time default” model for<br />

financial instruments in the<br />

collateralized debt obligations<br />

(CDOs) family<br />

Calculation of the present value of financial instruments as the current value<br />

of future cash flows (discounted at market interest rates), taking into<br />

account:<br />

• Estimate of prepayment rates:<br />

• Issuer credit risk; and<br />

• Current market interest rates.<br />

In the case of valuation of asset-backed securities (ABSs), future<br />

prepayments are calculated on the conditional prepayment rates that the<br />

issuers themselves provide.<br />

The “time-to-default” model is used to measure default probability. One of the<br />

main variables used is the correlation of defaults extrapolated from several<br />

index tranches (ITRAXX and CDX) with the underlying portfolio of our CDOs.<br />

• Prepayment rates.<br />

• Default correlation.<br />

• Credit spread (1)<br />

Trading portfolio<br />

Debt securities<br />

502<br />

Equity instruments 166<br />

Available-for-sale financial assets<br />

Debt securities 320<br />

• Equity instruments<br />

• Derivatives<br />

• Present-value method<br />

Trading derivatives for interest rate futures<br />

and forwards:<br />

• Present-value method.<br />

• “Libor Market” model.<br />

For variable income and foreign exchange<br />

options:<br />

• Monte Carlo simulations<br />

• Numerical integration<br />

• Heston<br />

• Credit baskets<br />

Net asset value (NAV) for hedge funds and for equity instruments listed in<br />

thin and less active markets<br />

The “Libor Market” model models the complete term structure of the interest<br />

rate curve, assuming a CEV (constant elasticity of variance) lognormal<br />

process. The CEV lognormal process is used to measure the presence of a<br />

volatility shift.<br />

The options are valued through generally accepted valuation models, to<br />

which the observed implied volatility is added.<br />

These models assume a constant diffusion of default intensity.<br />

• Credit spread (1)<br />

• NAV supplied by the<br />

fund manager.<br />

• Correlation decay (2).<br />

• Vol-of-vol. (3)<br />

• Reversion factor. (4)<br />

• Volatility Spot<br />

Correlation (5)<br />

• Defaults correlation.<br />

• Historical CDS volatility<br />

Equity instruments 209<br />

ASSETS<br />

Trading derivatives 245<br />

LIABILITIES<br />

Trading derivatives 98<br />

(1) Credit spread: The spread between the interest rate of a risk-free asset (e.g. Treasury securities) and the interest rate of any other security that is identical in every respect except for quality rating. Spreads are considered as Level 3 inputs when referring to<br />

illiquid issues. Based on spreads of similar entities.<br />

(2) Correlation decay: The constant rate of decay that allows us to calculate how the correlation evolves between the different pairs of forward rates.<br />

(3) Vol-of-Vol: Volatility of implicit volatility. This is a statistical measure of the changes of the spot volatility.<br />

(4) Reversion Factor: The speed with which volatility reverts to its natural value.<br />

(5) Volatility- Spot Correlation: a statistical measure of the linear relationship (correlation) between the spot price of a security and its volatility.<br />

67

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