# “ Substitution risk”

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“Substitution risk”Rocco LetterelliMarco TicciatiMsc in Finance

Slide2Substitution risk

Definition:“ risk of greater cost sostitution of the asset afforded by one part if the couterpart makes a default before the settlement date”In the financial lecterature there is relationships withPre-settlement riskConterparty risk

Slide3Substitution risk

It is a kind of risk which we have in hedging positionsIt is observable to OTC derivative marketsNeed for mark-to-market monitoring of financial position COST OF SUBSTITUTION ESTIMATION CURRENT EXPOSURE

Slide4Substitution riskmeasurement:

2

questions

:

If

a counterparty was to default today, what would it cost to replace the derivatives transaction (i.e., what is the current exposure

)?

If

a counterparty defaults at some point in the future, what is a reasonable estimate of the potential replacement cost (i.e., what is the potential exposure)?

Slide5Substitution risk:

1) the first

answer

is

quite

intuitive and

it

is

represented

by

mark

-to-market

value

of the

underlying

contract

.

Example

: 5y swap

fixed

rate

6%

floating

rate of LIBOR.

The

mark-to-market value

is zero at t

0

Suppose

that

t=0,5 the swap

rate for a 4.5-year swap is 5.50%. If the counterparty paying the fixed rate of 6.00% defaults, the

nondefaulting

counterparty receiving

the fixed rate (and paying the floating rate) will be forced to replace it with a 5.50% swap and will thereby suffer a replacement cost equal to 0.50% per annum for the remaining 4.5

years

Slide6Substitution risk:

2)

The

second question is more difficult to answer in that it asks for an assessment of what the replacement cost could be in the

future

Dealers use Monte Carlo or historical simulation studies, option valuation models, and other statistical techniques to assess potential

exposure. These

techniques are often used to generate two measures of potential exposure: expected exposure; and maximum or "worst case"

exposure

Slide72 important measures:

Expected exposure at any point during the life of the swap is the mean of all possible probability-weighted replacement costs, where the replacement cost in any outcome is equal to the mark-to-market present value if positive and zero if negative.The maximum potential exposure is calculated as an estimate of "worst case" exposure at any point in time

Slide8This

shape

is

due to 2

different

effects

:

Diffusion

effects

:

as the time progresses the probability to have MKT far from zero increases (volatility of underlying)

Amortization

effect

: the

reduction

in

years

of cash

flows

that

need

to be

replaced

Slide9Substitution risk

regulation…

Slide10Substitution risk

According to basel I there are two approaches to estimate counterparty risk Basel II treated CCR loss as credit riskThe second one accounts for substitution riskIt is based on

Slide11Substitution risk

the

CE is given by the current market value (MV) of

the OTC

contract, that is, by the cost the bank would face to replace the contract (“

substitutioncost

”) with an identical one, if the counterparty were to default. If the market value

is negative

, then there is no current exposure to credit risk, and CE is set to zero. To

this CE

, an estimate of FPE must be added, given by a fixed percentage (

p) of the notional

(

N). The value of p, also called the “add-on” factor, depends on the underlying asset

and

increases

with the maturity of the contract.

LEE = CE + FPE = max(0,MV ) + p ·N

Slide12Substitution risk

After the crisis… Basel III Basel III has incorporated credit value adjustment (CVA) that is the risk premium from the counterparty to be compensated for the risk of the counterparty defaulting , in calculations of regulatory capital for counterparty credit risk (CCR)

Slide13Substitution risk

Basel III applies a hybrid approach in terms of CCR regulation by treating default risk and credit migration risk differently: the default risk is treated as

creditrisk

under the ASRF framework (with capital horizon

H = 1 year

and confidence level

q = 99.9%), while the credit migration risk is

treated as market risk

Slide14Substitution risk

Therefore, in the last regulation framework MORE WEIGHT TO THE MARKET FEATURE OF CONTERPARTY RISK MORE WEIGHT OF SUBSTITUTION RISK

Slide15Slide16

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## “ Substitution risk”

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