8. Fair value of financial instruments
The fair value of a financial asset or liability on a given date is the amount for which it could be exchanged or settled, respectively, on that date between two knowledgeable, willing parties in an arm’s length transaction under market conditions. The most objective and common reference for the fair value of a financial asset or liability is the price that would be paid for it on an organized, transparent and deep market (“quoted price” or “market price”).
If there is no market price for a given financial asset or liability, its fair value is estimated on the basis of the price established in recent transactions involving similar instruments or, in the absence thereof, by using mathematical measurement models that are sufficiently tried and trusted by the international financial community. The estimates used in such models take into consideration the specific features of the asset or liability to be measured and, in particular, the various types of risk associated with the asset or liability. However, the limitations inherent in the measurement models and possible inaccuracies in the assumptions and parameters required by these models may mean that the estimated fair value of an asset or liability does not exactly match the price for which the asset or liability could be exchanged or settled on the date of its measurement.
The fair value of the financial derivatives included in the heldfortrading portfolios is based on daily quoted price if there is an active market for these financial derivatives. If for any reason their quoted price is not available on a given date, these financial derivatives are measured using methods similar to those used in overthecounter (OTC) markets.
The fair value of OTC derivatives (“present value” or “theoretical price”) is equal to the sum of future cash flows arising from the instrument, discounted at the measurement date; these derivatives are valued using methods recognized by international financial markets: the “net present value” (NPV) method, option price calculation models, etc.
Determining the fair value of financial instruments
Below is a comparison of the carrying amount of the Group’s financial assets and liabilities in the accompanying consolidated balance sheets and their respective fair values:
Download ExcelFair Value and Carrying Amount  Notes  Millions of Euros  

2012  2011  2010  
Carrying Amount  Fair Value  Carrying Amount  Fair Value  Carrying Amount  Fair Value  
ASSETS 







Cash and balances with central banks  9  37,434  37,434  30,939  30,939  19,981  19,981 
Financial assets held for trading  10  79,954  79,954  70,602  70,602  63,283  63,283 
Other financial assets designated at fair value through profit or loss  11  2,853  2,853  2,977  2,977  2,774  2,774 
Availableforsale financial assets  12  71,500  71,500  58,144  58,144  56,456  56,456 
Loans and receivables  13  383,410  403,606  381,076  389,204  364,707  371,359 
Heldtomaturity investments  14  10,162  9,860  10,955  10,190  9,946  9,189 
Fair value changes of the hedges items in portfolio hedges of interest rate risk  15  226  226  146  146  40  40 
Hedging derivatives  15  4,894  4,894  4,552  4,552  3,563  3,563 
LIABILITIES 







Financial assets held for trading  10  55,927  55,927  51,303  51,303  37,212  37,212 
Other financial liabilities designated at fair value through profit or loss  11  2,516  2,516  1,825  1,825  1,607  1,607 
Financial liabilities at amortized cost  23  506,487  504,267  497,904  473,886  453,164  453,504 
Fair value changes of the hedged items in portfolio hedges of interest rate risk.  15          (2)  (2) 
Hedging derivatives  15  2,968  2,968  2,710  2,710  1,664  1,664 
In the case of financial instruments whose carrying amount is not the same as their theoretical fair value, the fair value has been calculated as follows:
 The fair value of “Cash and balances with central banks” has been considered equivalent to its carrying amount, because they are mainly shortterm balances.
 The fair value of “Heldtomaturity investments” is equivalent to their quoted price in active markets.
 The fair values of “Loans and receivables” and “Financial liabilities at amortized cost” have been estimated by discounting estimated future cash flows using the market interest rates prevailing at each yearend.
 The “Fair value changes of the hedged items in portfolio hedges of interestrate risk” item in the accompanying consolidated balance sheets registers the difference between the carrying amounts of the hedged deposits lent, included under "Loans and Receivables", and the fair value calculated using internal models and observable variables of market data (see Note 15).
For financial instruments whose carrying amount is equivalent to their fair value, the measurement processes used are set forth below:
 Level 1: Measurement using market observable quoted prices for the financial instrument in question, secured from independent sources and referred to active markets. This level includes listed debt securities, listed equity instruments, some derivatives and mutual funds.
 Level 2: Measurement that applies techniques using inputs drawn from observable market data.
 Level 3: Measurement using techniques where some of the inputs are not taken from market observable data. As of December 31, 2012, the affected instruments accounted for approximately 0.20% of financial assets and 0.01% of the Group’s financial liabilities. Model selection and validation is undertaken by control areas outside the market units.
The following table shows the main financial instruments carried at fair value in the accompanying consolidated balance sheets, broken down by the measurement technique used to determine their fair value:
Download ExcelFair Value by Levels  Notes  Millions of Euros  

2012  2011  2010  
Level 1  Level 2  Level 3  Level 1  Level 2  Level 3  Level 1  Level 2  Level 3  
ASSETS 










Financial assets held for trading  10  30,944  48,597  412  22,986  46,915  700  28,914  33,568  802 
Loans and advances to customers 

244                 
Debt securities 

27,053  718  295  19,731  793  451  22,930  921  508 
Equity instruments 

2,713  140  70  2,033  97  68  5,034  92  134 
Trading derivatives 

934  47,740  47  1,222  46,025  182  950  32,555  160 
Other financial assets designated at fair value through profit or loss  11  2,768  86    2,358  619    2,326  448   
Loans and advances to credit institutions 

  24               
Debt securities 

692  62    647  61    624  64   
Equity instruments 

2,076      1,711  558    1,702  384   
Availableforsale financial assets  12  51,682  18,551  757  41,286  15,249  1,067  41,500  13,789  668 
Debt securities 

48,484  18,359  700  37,286  15,025  602  37,024  13,352  499 
Equity instruments 

3,198  192  57  4,000  224  465  4,476  437  169 
Hedging derivatives  15  111  4,784    289  4,263    265  3,298   
LIABILITIES 










Financial liabilities held for trading  10  7,371  48,519  38  5,813  45,467  23  4,961  32,225  25 
Trading derivatives 

791  48,519  38  1,202  45,467  23  916  32,225  25 
Short positions 

6,580      4,611      4,046     
Other financial liabilities designated at fair value through profit or loss  11    2,516      1,825      1,607   
Hedging derivatives  15    2,951  17    2,710    96  1,568   
The heading “Availableforsale financial assets” in the accompanying consolidated balance sheets as of December 31, 2012, 2011 and 2010 additionally includes €510 million, €541 million and €499 million, respectively, accounted for at cost, as indicated in the section of this Note entitled “Financial instruments at cost”.
The following table sets forth the main measurement techniques, hypothesis and inputs used in the estimation of fair value of the financial instruments classified under Levels 2 and 3, based on the type of financial asset and liability and the corresponding balances as of December 31, 2012:
Financial Instruments Level 2  Measurement techniques  Main assumptions  Main inputs used  2012 Fair value (millions of euros) 


Debt securities  Presentvalue method  Determining the present value of financial instruments as the current value of future cash flows (discounted at market interest rates), taking into account: • the estimate of prepayment rates; • the issuer credit risk; and • current market interest rates. • Net Asset Value (NAV) published recurrently, but not more frequently than every quarter. 
• Risk premiums. • Observable market interest rates 
Trading portfolio  
Debt securities  718  
Equity instruments  140  
Other financial assets at fair value through profit and loss  
Equity instruments  Debt securities  62  
Deposits from credit institutions  24  
Availableforsale financial assets  
Debt securities  18,359  
Equity instruments  192  
Other financial liabilities designated at fair value through profit or loss  2,516  
Derivatives  Analytic/semianalytic formulae  For share, currency, inflation or commodity derivatives: • The BlackScholes assumptions take into account possible convexity adjustments For interest rate derivatives: • BlackScholes assumptions apply a lognormal process for forward rates and consider possible convexity adjustments. 
For share, inflation, currency or commodity derivatives: • Forward structure of the underlying asset. • Volatility of options. • Observable correlations between underlying assets. For interestrate derivatives: • The term structure of interest rates. • Volatility of underlying asset. For credit derivatives: • Credit default swap (CDS) prices. • Historical CDS volatility. 
Assets  
Trading derivatives  47,740  
Hedging derivatives  4,784  
For share, currency or commodity derivatives: • Monte Carlo simulations. 
Local volatility model: assumes a constant diffusion of the underlying asset with the volatility depending on the value of the underlying asset and the term  Liabilities  
For interestrate derivatives: • BlackDermanToy Model, Libor Market Model and SABR. • HW 1 factor 
This model assumes that: • The forward rates in the term structure of the interest rate curve are perfectly correlated. 
Trading derivatives  48,519  
For credit derivatives: • Diffusion models. 
These models assume a constant diffusion of default intensity.  Hedging derivatives  2,951 
Financial Instruments Level 3  Measurement techniques  Main assumptions  Main unobservable inputs  2012 Fair value (millions of euros) 


Debt securities  Presentvalue method “Time default” model for financial instruments in the collateralized debt obligations (CDO) family. 
Determining the current value of financial instruments as the current value of future cash flows (discounted at market interest rates), taking into account: • estimate of prepayment rates; • issuer credit risk; and • current market interest rates. In the case of measurement of assetbacked securities (ABS), the future prepayments are calculated according to conditional prepayment rates supplied by the issuers themselves. The "timetodefault" model is used to measure the probability of default. One of the main variables used is the correlation of defaults extrapolated from several index tranches (ITRA00 and CDX) with the underlying portfolio of our CDOs. 
• Prepayment rates • Default correlation • Credit spread (1) 
Trading portfolio  
Debt securities  295  
Equity instruments  70  
Availableforsale financial assets  
Debt securities  700  
Equity instruments  • Presentvalue method  Net asset value (NAV) for hedge funds and for equity instruments listed in thin or less active markets  • Credit spread ^{(1)} • NAV supplied by the fund administrator or issuer of the securities. 
Equity instruments  57 
Trading derivatives  Trading derivatives for interest rate futures and forwards: • Presentvalue method • “Libor Market” model. 
The "Libor Market” model models the complete term structure of the interestrate curve, assuming a constant elasticity of variance (CEV) lognormal process. The CEV lognormal process is used to measure the presence of a volatility shift.  Correlation decay ^{(2)}  Assets  
For variable income and foreign options: • Monte Carlo simulations • Numerical integration • Heston 
The options are measured through generally accepted valuation models, to which the observed implied volatility is added.  • VolofVol ^{(3)} • Reversion factor ^{(4)} • Volatility Spot Correlation^{ (5)} 
Trading derivatives  47  
Liabilities  
• Credit baskets  These models assume a constant diffusion of default intensity.  • Default correlation. • Historical CDS volatility 
Trading derivatives Hedging derivatives 
38 17 
The changes in the balance of Level 3 financial assets and liabilities included in the accompanying consolidated balance sheets are as follows:
Download ExcelFinancial Assets Level 3 Changes in the Period 
Millions of Euros  

2012  2011  2010  

Assets  Liabilities  Assets  Liabilities  Assets  Liabilities 
Balance at the beginning  1,767  23  1,469  25  1,707  96 
Valuation adjustments recognized in the income statement (*)  50  2  (1)  (12)  (123)  12 
Valuation adjustments not recognized in the income statement  (3)        (18)   
Acquisitions, disposals and liquidations  (278)  29  268  9  (334)  (100) 
Net transfers to Level 3  (134)    33    236   
Exchange differences and others  (233)  1  (2)  1  1  17 
Exchange differences and others  1,169  55  1,767  23  1,469  25 
As of December 31, 2012, the profit/loss on sales of financial instruments classified as level 3 recognized in the accompanying income statement was insignificant.
The financial instruments transferred between the different levels of measurement in 2012 are at the following amounts in the accompanying consolidated balance sheets as of December 31, 2012:
Download ExcelTransfer between levels  From: To: 
Millions of Euros  

Level I  Level 2  Level 3  
Level 2  Level 3  Level 1  Level 3  Level 1  Level 2  
ASSETS 







Financial assets held for trading 

           
Availableforsale financial assets 

78    454  18  12  137 
LIABILITIES 







As of December 31, 2012, the effect on the consolidated income and consolidated equity of changing the main hypotheses used for the measurement of Level 3 financial instruments for other reasonably possible models, taking the highest (most favorable hypotheses) or lowest (least favorable hypotheses) value of the range deemed probable, would be as follows:
Download ExcelFinancial Assets Level 3 Sensitivity Analysis  Millions of Euros  

Potential Impact on Consolidated Income Statement  Potential Impact on Total Equity  
Most Favorable Hypotheses  Least Favorable Hypotheses  Most Favorable Hypotheses  Least Favorable Hypotheses  
ASSETS 




Financial assets held for trading  22  (15)     
Availableforsale financial assets      10  (10) 
LIABILITIES 




Financial liabilities held for trading  4  (4)     
Total  26  (19)  10  (10) 
Loans and financial liabilities at fair value through profit or loss
As of December 31, 2012, 2011 and 2010, there were no loans or financial liabilities at fair value other than those recognized under the headings “Financial assets held for trading  Loans and advances to customers”, "Other financial assets designated at fair value through profit or loss" and "Other financial liabilities designated at fair value through profit or loss" in the accompanying consolidated balance sheets.
Financial instruments at cost
As of December 31, 2012, 2011 and 2010, equity instruments, derivatives with these equity instruments as underlying assets, and certain discretionary profitsharing arrangements in some companies, were recognized at cost in the Group’s consolidated balance sheets because their fair value could not be reliably determined, as they are not traded in organized markets and thus their unobservable inputs are significant. On the above dates, the balance of these financial instruments recognized in the portfolio of availableforsale financial assets amounted to €510 million, €541 million and €499 million, respectively.
The table below outlines the financial assets and liabilities carried at cost that were sold in 2012, 2011 and 2010:
Download ExcelSales of financial instruments at cost  Millions of Euros  

2012  2011  2010  
Amount of Sale  29  19  51 
Carrying Amount at Sale Date  5  8  36 
Gains/Losses  24  11  15 