Response to cP on EBA launches consultation on technical standards on the standardised approach for counterparty credit risk
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We recommend a shift between 1% and 3%. This is because, if the shift is too small, the mean of the log normal distribution will be too close to zero, generating an inappropriate distribution with a big density around zero. Thus, in order to have a reasonable probability distribution and meaningful prices, the shift should be large enough.
Having a dynamic lambda is a good way to design a lambda that works in all cases (or almost, apart for very negative strikes in case of option 3a).
It becomes unnecessary to set up a process to monitor the rates, and change the lambda when needed, which will raise more questions around when to trigger the change, and what should be the level of the new lambda.
Thus, the proposed methodology seems more practical and simpler to put in place.
raise some concerns:
There are no concerns with setting the shift λ according to the prevalent market conditions.
The ATM price is given by the Black-Scholes (“BS”) formula:
ATM price = BS(σ, Fwd + λ, Fwd + λ, t)
Where σ is the volatility parameter, Fwd is the forward rate, λ is the shift parameter
If λ changes to λ’, then σ needs to be changed to σ’, where:
BS(σ, Fwd + λ, Fwd + λ, t) = BS(σ’, Fwd + λ’, Fwd + λ’, t)
As a first order approximation, this equation can be simplified to: σ * (fwd + λ) = σ’ * (fwd + λ’)
Which one of the three options (option 4a: 1 bp, option 4b: 0.1% or option 4c: 1%) do you think is more appropriate as a threshold? Please provide the rationale for the chosen option.
We believe that Option 4c: 1% is more appropriate as a threshold. This is because, it is the option which generates a reasonable probability distribution.We recommend a shift between 1% and 3%. This is because, if the shift is too small, the mean of the log normal distribution will be too close to zero, generating an inappropriate distribution with a big density around zero. Thus, in order to have a reasonable probability distribution and meaningful prices, the shift should be large enough.
Please provide examples of cases where the possibility to set the shift ? according to the prevalent market conditions (option 4) might: - provide some benefits - raise some concerns
provide some benefits:Having a dynamic lambda is a good way to design a lambda that works in all cases (or almost, apart for very negative strikes in case of option 3a).
It becomes unnecessary to set up a process to monitor the rates, and change the lambda when needed, which will raise more questions around when to trigger the change, and what should be the level of the new lambda.
Thus, the proposed methodology seems more practical and simpler to put in place.
raise some concerns:
There are no concerns with setting the shift λ according to the prevalent market conditions.
Do you consider necessary an adjustment to the supervisory volatility parameter ? as defined in Article 5? In the case an adjustment is considered necessary, how should it be carried out?
We do consider it necessary to make an adjustment to the supervisory volatility parameter σ as defined in Article 5. This is because, when the shift changes, this will impact the ATM price. Hence, the volatility needs to be changed in order to reflect that. The adjustment should be carried out in order to fit the same ATM price.The ATM price is given by the Black-Scholes (“BS”) formula:
ATM price = BS(σ, Fwd + λ, Fwd + λ, t)
Where σ is the volatility parameter, Fwd is the forward rate, λ is the shift parameter
If λ changes to λ’, then σ needs to be changed to σ’, where:
BS(σ, Fwd + λ, Fwd + λ, t) = BS(σ’, Fwd + λ’, Fwd + λ’, t)
As a first order approximation, this equation can be simplified to: σ * (fwd + λ) = σ’ * (fwd + λ’)