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Fair Value of Financial Instruments
 12 Months Ended
Oct. 31, 2025
Text Block [Abstract]  
Fair Value of Financial Instruments
6
Fair Value of Financial Instruments
Determination of fair value
The calculation of fair value is based on market conditions at a specific point in time and therefore may not be reflective of future fair values. The Bank has controls and processes in place to ensure that the valuation of financial instruments is appropriately determined.
The Bank discloses the classification of all financial instruments carried at fair value in a hierarchy based on the determination of fair value. The best evidence of fair value for a financial instrument is the quoted price in an active market. Fair value based on unadjusted quoted market prices for identical instruments in active markets represents a Level 1 valuation. Where possible, valuations are based on quoted prices or observable inputs obtained from active markets.
Independent Price Verification (IPV) is undertaken to assess the accuracy of prices and inputs used in the determination of fair value. The IPV process is performed by price verification groups that are independent of the business. The Bank maintains a list of approved pricing sources that are used in the IPV process. These sources include, but are not limited to, brokers, exchanges and pricing services. The valuation policies relating to the IPV process require that all pricing or rate sources used be external to the Bank. At least annually, an independent assessment of pricing or rate sources is performed to determine the market presence and reliability of market levels.
Quoted prices are not always available for
over-the-counter
(OTC) transactions as well as for transactions in inactive or illiquid markets. OTC transactions are valued using internal models that maximize the use of observable inputs to estimate fair value. The chosen valuation technique incorporates all the factors that market participants would take into account in pricing a transaction. When fair value is based on all significant market observable inputs, the valuation is classified as Level 2. Financial instruments traded in a less active market can be valued using indicative market prices, the present value of cash flows or other valuation techniques. Fair value estimates normally do not consider forced or liquidation sales.
Where financial instruments trade in inactive markets or when using models where observable parameters do not exist, significant management judgment is required for valuation methodologies and model inputs. Valuations that require the significant use of unobservable inputs are considered Level 3.
The specific inputs and valuation techniques used in determining the fair value of financial instruments are noted below. For Level 3 instruments, additional information is disclosed in the Level 3 sensitivity analysis on page 173.
The fair values of cash and deposits with banks, securities purchased under resale agreements and securities borrowed, customers’ liability under acceptances, obligations related to securities sold under repurchase agreements and securities lent, acceptances, and obligations related to securities sold short are assumed to approximate their carrying values, either due to their short-term nature or because they are frequently repriced to current market rates.
Trading loans
Trading loans are comprised of loans that serve as hedges to total return swaps, hedges for precious metal certificate liabilities and loans subject to sale through syndication. Trading loans that serve as hedges to loan-based credit total return swaps and precious metals certificate liabilities are valued using consensus prices from Bank approved independent pricing services. The fair value of loans subject to sale through syndication approximates their carrying value due to the short-term nature of these loans.
Government issued or guaranteed securities
The fair values of government issued or guaranteed debt securities are primarily based on unadjusted quoted prices in active markets, where available. Where quoted prices in active markets are not available, the fair value is determined by utilizing recent transaction prices, reliable broker quotes, or pricing services, which derive fair values using only observable valuation inputs, which are significant to the fair values.
 
 
For securities for which quoted prices are not available, the Bank uses a discounted cash flow method, using the effective yield of a similar instrument adjusted for instrument-specific risk factors that are observable inputs such as credit spread and contracted features.
Corporate and other debt
Corporate and other debt securities are valued using unadjusted quoted prices from independent market data providers or third-party broker quotes from an active market. Where direct prices from active markets are not available, the valuation is performed with a yield-based valuation approach. In some instances, interpolated yields of similar bonds are used to price securities. The Bank uses pricing models with observable inputs from market sources such as credit spread, and interest rate curves. These inputs are verified through an IPV process on a monthly basis.
For certain securities where there is no active market, no consensus market pricing and no indicative or executable independent third-party quotes, the Bank uses pricing by third-party providers or internal pricing models and cannot readily observe the significant inputs used to price such instruments.
Mortgage-backed securities
The fair value of residential mortgage-backed securities is primarily determined using broker quotes and independent market data providers. In limited circumstances, an internal price-based model may be used with the unobservable inputs that are significant to the fair value.
Equity securities
The fair value of equity securities is based on unadjusted quoted prices in active markets, where available. Where equity securities are less frequently traded, the most recent exchange-quoted pricing is used to determine fair value.
For private equity securities, where quoted prices in active markets are not readily available, the fair value is determined as a multiple of the underlying earnings or percentage of underlying net asset value obtained from third-party general partner statements.
Derivatives
Fair values of exchange-traded derivatives are based on unadjusted quoted market prices from an active market. Fair values of
over-the-counter
(OTC) derivatives or inactive exchange-traded derivatives are determined using pricing models, which take into account observable valuation inputs such as current market and contractual prices of the underlying instruments, as well as time value and yield curve or volatility factors underlying the positions. The determination of the fair value of derivatives includes consideration of credit risk, estimated funding costs and ongoing direct costs over the life of the instruments.
Derivative products valued using a valuation technique with market-observable inputs mainly include interest rate swaps and options, currency swaps and forward foreign exchange contracts. The most frequently applied valuation techniques include forward pricing and swap models, using present value calculations. The models incorporate various inputs including foreign exchange spot, forward rates and interest rate curves.
Derivative products valued using a valuation technique with significant unobservable inputs, such as volatility, correlation, and forward curves, may include long dated contracts (interest rate swaps, currency swaps, option contracts, commodity contracts and certain credit default swaps) and other derivative products that reference a basket of assets.
Loans
The estimated fair value of loans carried at amortized cost reflects changes in the general level of interest rates and creditworthiness of borrowers that have occurred since the loans were originated or purchased. The particular valuation methods used are as follows:
 
  •  
Canadian fixed rate residential mortgages are fair valued by discounting the expected future contractual cash flows, taking into account expected prepayments and using management’s best estimate of average market interest rates currently offered for mortgages with similar remaining terms.
  •  
For fixed rate business and government loans, fair value is determined by discounting the expected future contractual cash flows at market interest rates for loans with similar credit risks.
  •  
For all other fixed rate loans, fair value is determined by discounting the expected future contractual cash flows of these loans at market interest rates.
  •  
For all floating rate loans fair value is assumed to equal carrying value.
The fair value of loans is not adjusted for the value of any credit protection the Bank has purchased to mitigate credit risk.
Deposits
The fair values of deposits payable on demand or after notice or floating rate deposits payable on a fixed date is assumed to equal carrying value.
The estimated fair values of Canadian personal fixed rate deposits payable on a fixed date are fair valued by discounting the expected future contractual cash outflows, using management’s best estimate of average market interest rates currently offered for deposits with similar remaining terms.
Deposits under the Canada Mortgage Bond (CMB) program are fair valued by discounting expected future contractual cash flows using market observable inputs.
For all other fixed rate deposits, fair value is determined by discounting the expected future contractual cash flows of these deposits at interest rates currently offered for deposits with similar terms.
For structured notes containing embedded features that are bifurcated from plain vanilla notes, the fair value of the embedded derivatives is determined using option pricing models with observable inputs similar to other interest rate or equity derivative contracts.
Certain deposits that are designated at FVTPL are structured notes. Their coupon or repayment terms can be linked to the performance of market parameters such as interest rates, equities, and foreign currencies. The fair value of these structured notes is determined using models which incorporate observable market inputs, such as interest rate curves, equity prices, equity volatility and foreign exchange rates. Some structured notes may have significant unobservable inputs to model valuation such as interest rate volatility and equity correlation.
Obligations related to securities sold short
The fair values of these obligations are based on the fair value of the underlying securities, which can include debt or equity securities. The method used to determine fair value is based on the quoted market prices where available in an active market.
 
 
Subordinated debentures and other liabilities
The fair values of subordinated debentures, including debentures issued by subsidiaries which are included in other liabilities, are determined by reference to quoted market prices where available or market prices for debt with similar terms and risks. The fair values of other liabilities are determined by the discounted contractual cash flow method with appropriate currency swap curves for the remaining term or market prices for instruments with similar terms and risks.
Fair value of financial instruments
The following table sets out the fair values of financial instruments of the Bank using the valuation methods and assumptions described above. The fair values disclosed do not include
non-financial
assets, such as property and equipment, investments in associates, precious metals, goodwill and other intangible assets.
 
   
2025
    
2024
  
As at October 31 ($ millions)  
Total
fair
value
    
Total
carrying
value
    
Total
fair
value
    
Total
carrying
value
  
Assets:
        
Cash and deposits with financial institutions
  
$
65,967
 
  
$
65,967
 
   $ 63,860     $ 63,860  
Trading assets
  
 
152,223
 
  
 
152,223
 
     129,727       129,727  
Securities purchased under resale agreements and securities borrowed
  
 
203,008
 
  
 
203,008
 
     200,543       200,543  
Derivative financial instruments
  
 
46,531
 
  
 
46,531
 
     44,379       44,379  
Investment securities – FVOCI and FVTPL
  
 
126,226
 
  
 
126,226
 
     123,420       123,420  
Investment securities – Amortized cost
  
 
23,239
 
  
 
23,722
 
     28,422       29,412  
Loans
  
 
769,900
 
  
 
771,045
 
      757,825        760,829  
Customers’ liability under acceptances
  
 
177
 
  
 
177
 
     148       148  
Other financial assets
  
 
28,128
 
  
 
28,128
 
     22,467       22,467  
Liabilities:
        
Deposits
  
 
 965,925
 
  
 
 966,279
 
     941,290       943,849  
Financial instruments designated at fair value through profit or loss
  
 
47,165
 
  
 
47,165
 
     36,341       36,341  
Acceptances
  
 
178
 
  
 
178
 
     149       149  
Obligations related to securities sold short
  
 
38,104
 
  
 
38,104
 
     35,042       35,042  
Derivative financial instruments
  
 
56,031
 
  
 
56,031
 
     51,260       51,260  
Obligations related to securities sold under repurchase agreements and
securities lent
  
 
189,144
 
  
 
189,144
 
     190,449       190,449  
Subordinated debentures
  
 
7,749
 
  
 
7,692
 
     7,814       7,833  
Other financial liabilities
  
 
56,500
 
  
 
56,529
 
     53,342       53,387  
Changes in interest rates, credit spreads and liquidity costs are the main cause of changes in the fair value of the Bank’s financial instruments resulting in a favourable or unfavourable variance compared to carrying value. For the Bank’s financial instruments carried at cost or amortized cost, the carrying value is not adjusted to reflect increases or decreases in fair value due to market fluctuations, including those due to interest rate changes. For FVOCI investment securities, derivatives and financial instruments measured at FVTPL or designated as fair value through profit or loss, the carrying value is adjusted regularly to reflect the fair value.
 
 
Fair value hierarchy
The following table outlines the fair value hierarchy of instruments carried at fair value on a recurring basis and of instruments not carried at fair value.
 
   
2025
    
2024
  
As at October 31 ($ millions)  
Level 1
    
Level 2
    
Level 3
    
Total
    
Level 1
    
Level 2
    
Level 3
    
Total
  
Instruments carried at fair value on a recurring basis:
                
Assets:
                
Precious metals
(1)
  
$
–
 
  
$
5,156
 
  
$
–
 
  
$
5,156
 
   $ –     $ 2,540     $ –     $ 2,540  
Trading assets
                
Loans
  
 
–
 
  
 
8,486
 
  
 
1
 
  
 
8,487
 
     –       7,649       –       7,649  
Canadian federal government and government guaranteed debt
  
 
13,838
 
  
 
1,963
 
  
 
–
 
  
 
15,801
 
     11,229       3,742       –       14,971  
Canadian provincial and municipal debt
  
 
8,374
 
  
 
3,336
 
  
 
–
 
  
 
11,710
 
     6,228       2,185       –       8,413  
U.S. treasury and other U.S. agencies’ debt
  
 
9,132
 
  
 
–
 
  
 
–
 
  
 
9,132
 
     15,050       –       –       15,050  
Other foreign governments’ debt
  
 
1,837
 
  
 
8,451
 
  
 
–
 
  
 
10,288
 
     422       9,932       –       10,354  
Corporate and other debt
  
 
3,523
 
  
 
6,593
 
  
 
–
 
  
 
10,116
 
     4,940       6,990       4       11,934  
Equity securities
  
 
83,412
 
  
 
373
 
  
 
12
 
  
 
83,797
 
     59,081       88       21       59,190  
Other
  
 
–
 
  
 
2,892
 
  
 
–
 
  
 
2,892
 
     –       2,166       –       2,166  
 
$
 120,116
 
  
$
32,094
 
  
$
13
 
  
$
 152,223
 
   $  96,950     $  32,752     $ 25     $  129,727  
Investment securities
(2)
                
Canadian federal government and government guaranteed debt
  
$
15,143
 
  
$
7,967
 
  
$
–
 
  
$
23,110
 
   $ 12,739     $ 8,801     $ –     $ 21,540  
Canadian provincial and municipal debt
  
 
16,293
 
  
 
4,550
 
  
 
–
 
  
 
20,843
 
     12,823       4,702       –       17,525  
U.S. treasury and other U.S. agencies’ debt
  
 
 42,300
 
  
 
6,736
 
  
 
–
 
  
 
49,036
 
     39,999       6,377       –       46,376  
Other foreign governments’ debt
  
 
7,099
 
  
 
20,627
 
  
 
–
 
  
 
27,726
 
     3,940       25,346       –       29,286  
Corporate and other debt
  
 
116
 
  
 
2,892
 
  
 
32
 
  
 
3,040
 
     133       3,359       35       3,527  
Equity securities
  
 
96
 
  
 
329
 
  
 
2,046
 
  
 
2,471
 
     2,983       317       1,866       5,166  
 
$
81,047
 
  
$
43,101
 
  
$
2,078
 
  
$
126,226
 
   $ 72,617     $ 48,902     $ 1,901     $ 123,420  
Derivative financial instruments
                
Interest rate contracts
  
$
–
 
  
$
9,804
 
  
$
3
 
  
$
9,807
 
   $ –     $ 11,584     $ –     $ 11,584  
Foreign exchange and gold contracts
  
 
–
 
  
 
26,411
 
  
 
1
 
  
 
26,412
 
     –       26,004       –       26,004  
Equity contracts
  
 
816
 
  
 
6,452
 
  
 
161
 
  
 
7,429
 
     150       4,313       44       4,507  
Credit contracts
  
 
–
 
  
 
269
 
  
 
4
 
  
 
273
 
     –       180       2       182  
Commodity contracts
  
 
–
 
  
 
2,594
 
  
 
16
 
  
 
2,610
 
     –       2,095       7       2,102  
 
$
816
 
  
$
45,530
 
  
$
185
 
  
$
46,531
 
   $ 150     $ 44,176     $ 53     $ 44,379  
Liabilities:
                
Deposits
(3)
  
$
–
 
  
$
335
 
  
$
–
 
  
$
335
 
   $ –     $ 193     $ –     $ 193  
Financial liabilities designated at fair
value through profit or loss
  
 
–
 
  
 
47,165
 
  
 
–
 
  
 
47,165
 
     –       36,341       –       36,341  
Obligations related to securities sold short
  
 
34,864
 
  
 
3,240
 
  
 
–
 
  
 
38,104
 
     30,721       4,319       2       35,042  
Derivative financial instruments
                
Interest rate contracts
  
 
–
 
  
 
17,181
 
  
 
8
 
  
 
17,189
 
     –       17,895       13       17,908  
Foreign exchange and gold contracts
  
 
–
 
  
 
25,793
 
  
 
–
 
  
 
25,793
 
     –       25,900       –       25,900  
Equity contracts
  
 
783
 
  
 
9,288
 
  
 
43
 
  
 
10,114
 
     139       4,687       19       4,845  
Credit contracts
  
 
–
 
  
 
24
 
  
 
2
 
  
 
26
 
     –       46       1       47  
Commodity contracts
  
 
–
 
  
 
2,897
 
  
 
12
 
  
 
2,909
 
     –       2,550       10       2,560  
 
$
783
 
  
$
55,183
 
  
$
65
 
  
$
56,031
 
   $ 139     $ 51,078     $ 43     $ 51,260  
Instruments not carried at fair value
(4)
:
                
Assets:
                
Investment securities – amortized cost
  
$
1,548
 
  
$
21,691
 
  
$
–
 
  
$
23,239
 
   $ 1,127     $ 27,295     $ –     $ 28,422  
Loans
(5)
  
 
–
 
  
 
–
 
  
 
 400,574
 
  
 
400,574
 
     –       –        399,139       399,139  
Liabilities:
                
Deposits
(5)
  
 
–
 
  
 
 392,222
 
  
 
–
 
  
 
392,222
 
     –       411,838       –       411,838  
Subordinated debentures
  
 
7,345
 
  
 
404
 
  
 
–
 
  
 
7,749
 
     –       7,814       –       7,814  
Other liabilities
  
 
–
 
  
 
22,098
 
  
 
486
 
  
 
22,584
 
     –       21,563       499       22,062  
 
(1)
The fair value of precious metals is determined based on quoted market prices and forward spot prices, where applicable, less the cost to sell.
(2)
Excludes debt investment securities measured at amortized cost of $23,722 (October 31, 2024 – $29,412).
(3)
These amounts represent embedded derivatives bifurcated from structured note liabilities measured at amortized cost.
(4)
Represents the fair value of financial assets and liabilities where the carrying amount is not a reasonable approximation of fair value.
(5)
Represents fixed rate instruments.
 
 
Level 3 instrument fair value changes
Financial instruments categorized as Level 3 in the fair value hierarchy as at October 31, 2025, comprised of loans, structured corporate bonds, equity securities and derivatives.
The following table summarizes the changes in Level 3 instruments carried at fair value for the year ended October 31, 2025.
All positive balances represent assets and negative balances represent liabilities. Consequently, positive amounts indicate purchases of assets or settlements of liabilities and negative amounts indicate sales of assets or issuances of liabilities.
 
   
As at October 31, 2025
  
($ millions)  
Fair value
November 1
2024
    
Gains/(losses)
recorded in
income
(1)
    
Gains/(losses)
recorded in
OCI
    
Purchases/
Issuances
    
Sales/
Settlements
    
Transfers
into/out of
Level 3
    
Fair value
October 31
2025
    
Change in
unrealized
gains/(losses)
recorded in
income for
instruments
still held
(2)
  
Trading assets
                
Loans
   $ –    
$
   –
 
  
$
   –
 
  
$
1
 
  
$
(179
)
  
$
179
 
  
$
1
 
  
$
   –
 
Corporate and other debt
     4    
 
–
 
  
 
–
 
  
 
–
 
  
 
–
 
  
 
(4
)
  
 
–
 
  
 
–
 
Equity securities
     21    
 
–
 
  
 
–
 
  
 
7
 
  
 
(19
)
  
 
3
 
  
 
12
 
  
 
1
 
    25    
 
–
 
  
 
–
 
  
 
8
 
  
 
(198
)
  
 
178
 
  
 
13
 
  
 
1
 
   
Investment securities
                
Corporate and other debt
     35    
 
(5
) 
  
 
–
 
  
 
–
 
  
 
–
 
  
 
2
 
  
 
32
 
  
 
(5
) 
Equity securities
     1,866    
 
148
 
  
 
69
 
  
 
197
 
  
 
(228
) 
  
 
(6
) 
  
 
2,046
 
  
 
141
 
     1,901    
 
143
 
  
 
69
 
  
 
197
 
  
 
(228
) 
  
 
(4
) 
  
 
 2,078
 
  
 
136
 
   
Derivative financial instruments – assets
                
Interest rate contracts
     –    
 
2
 
  
 
–
 
  
 
4
 
  
 
(3
)
  
 
–
 
  
 
3
 
  
 
2
(
4
)
 
Foreign exchange and gold contracts
     –    
 
–
 
  
 
–
 
  
 
2
 
  
 
–
 
  
 
(1
)
  
 
1
 
  
 
–
 
Equity contracts
     44    
 
97
 
  
 
–
 
  
 
17
 
  
 
–
 
  
 
3
 
  
 
161
 
  
 
97
(3)
 
Credit contracts
     2    
 
(1
)
  
 
–
 
  
 
3
 
  
 
–
 
  
 
–
 
  
 
4
 
  
 
(1
) 
Commodity contracts
     7    
 
9
 
  
 
–
 
  
 
–
 
  
 
–
 
  
 
–
 
  
 
16
 
  
 
9
 
   
Derivative financial instruments – liabilities
                
Interest rate contracts
     (13 )   
 
(10
) 
  
 
–
 
  
 
(5
) 
  
 
22
 
  
 
(2
) 
  
 
(8
) 
  
 
(10
)
(4)
 
Equity contracts
     (19 )   
 
(15
) 
  
 
–
 
  
 
(26
) 
  
 
–
 
  
 
17
 
  
 
(43
) 
  
 
(15
)
(3)
 
Credit contracts
     (1 )   
 
1
 
  
 
–
 
  
 
(2
) 
  
 
–
 
  
 
–
 
  
 
(2
) 
  
 
1
 
Commodity contracts
     (10 )   
 
(2
) 
  
 
–
 
  
 
–
 
  
 
–
 
  
 
–
 
  
 
(12
) 
  
 
(2
) 
    10    
 
81
 
  
 
–
 
  
 
(7
)
  
 
19
 
  
 
17
 
  
 
120
 
  
 
81
 
Obligations related to securities sold short
     (2 )   
 
–
 
  
 
–
 
  
 
–
 
  
 
–
 
  
 
2
 
  
 
–
 
  
 
–
 
Total
   $ 1,934    
$
224
 
  
$
69
 
  
$
 198
 
  
$
 (407
) 
  
$
 193
 
  
$
2,211
 
  
$
218
 
 
(1)
Gains or losses for items in Level 3 may be offset with losses or gains on related hedges in Level 1 or Level 2.
(2)
These amounts represent the unrealized gains and losses from fair value changes of Level 3 instruments still held at the end of the period that are recorded in the Consolidated Statement of Income.
(3)
Certain unrealized gains and losses on derivative assets and liabilities are largely offset by
mark-to-market
changes on other instruments included in trading revenues in the Consolidated Statement of Income, since these instruments act as an economic hedge to certain derivative assets and liabilities.
(4)
Certain unrealized gains and losses on interest rate derivative contracts are largely offset by mark-to-market changes on embedded derivatives on certain deposit liabilities in the Consolidated Statement of Income.
The following table summarizes the changes in Level 3 instruments carried at fair value for the year ended October 31, 2024.
 
   
As at October 31, 2024
  
($ millions)  
Fair value
November 1
2023
    
Gains/(losses)
recorded in
income
(1)
    
Gains/(losses)
recorded
in OCI
    
Purchases/
Issuances
    
Sales/
Settlements
    
Transfers
into/out of
Level 3
    
Fair value
October 31
2024
  
Trading assets
     20       (1 )      –       44       (22 )      (16 )      25  
Investment securities
     1,749       100       (25 )      251       (207 )      33       1,901  
Derivative financial instruments
     15       (11 )      –       9       (9 )      6       10  
Obligations related to securities sold short
     –       –       –       –       –       (2 )      (2 ) 
 
(1)
Gains or losses for items in Level 3 may be offset with losses or gains on related hedges in Level 1 or Level 2.
Significant transfers
Significant transfers can occur between the fair value hierarchy levels when additional or new information regarding valuation inputs and their refinement and observability becomes available. The Bank recognizes transfers between levels of the fair value hierarchy at the end of the reporting period during which the change has occurred.
The following significant transfers made between Levels 1 and 2 were based on whether the fair value was determined using quoted market prices from an active market.
 
 
During the year ended October 31, 2025:
 
  •  
Trading assets of $620 million, investment securities of $2,310 million and obligations related to securities sold short of $265 million were transferred out of Level 2 into Level 1.
  •  
Trading assets of $914 million, investment securities of $1,532 million and obligations related to securities sold short of $268 million were transferred out of Level 1 into Level 2.
During the year ended October 31, 2024:
 
  •  
Trading assets of $1,867 million, investment securities of $3,010 million and obligations related to securities sold short of $396 million were transferred out of Level 2 into Level 1.
  •  
Trading assets of $712 million, investment securities of $698 million and obligations related to securities sold short of $6 million were transferred out of Level 1 into Level 2.
There was
no
significant transfer into and out of Level 3 during the year ended October 31, 2025 and October 31, 2024.
Level 3 sensitivity analysis
The table below sets out information about significant unobservable inputs used in measuring financial instruments categorized as Level 3 in the fair value hierarchy.
 
    
Valuation technique
       
Significant unobservable inputs
       
Range of estimates for
unobservable inputs
(1)
         
Changes in fair value
from reasonably
possible alternatives
($ millions)
       
Investment securities
      
General Partner valuations
        
       
Private equity securities
(2)
   Market comparable  
 
   per net asset value  
 
     n/a    
 
   (84)/84
       
Derivative financial instruments
              
       
Interest rate contracts
  
Option pricing
    
Interest rate
        
 
   model  
 
   volatility  
 
    
59% - 220%
    
 
   (1)/1
       
Equity contracts
  
Option pricing
     Equity volatility      
5% - 397%
      
 
   model  
 
   Equity correlation  
 
    
(114%) - 114%
    
 
   (45)/45
Commodity contracts
   Discounted cash flow  
 
   Forward curves  
 
    
9% - 15%
    
 
   (5)/5
 
(1)
The range of estimates represents the actual lowest and highest level inputs used to fair value financial instruments within each financial statement category.
(2)
The valuation of private equity securities utilizes net asset values as reported by fund managers. Net asset values are not considered observable as the Bank cannot redeem these instruments at such values. The range for net asset values per unit or price per share has not been disclosed for these instruments since the valuations are not model-based.
The Bank applies judgment in determining unobservable inputs used to calculate the fair value of Level 3 instruments.
The following section discusses the significant unobservable inputs for Level 3 instruments.
General Partner (GP) Valuations per Net Asset Value
Net asset values provided by GPs represent the fair value of investments in private equity securities.
Correlation
Correlation becomes an input into equity derivative pricing when the relationship between price movements of two or more of the underlying assets is relevant.
Volatility
Volatility for equity derivatives is a measure of the underlying price fluctuation. Interest rate volatility measures variability of a security yield or interest rate. Historic volatility is often calculated as the annualized standard deviation of daily price or yield variation for a given time period. Implied volatility is such that, when input into an option pricing model, returns a value equal to the current market value of the option.
Forward curves
Monthly forward curves for commodity contracts are required inputs to valuation. A portion of the forward curves are unobservable.