# Substitution risk Rocco Letterelli Marco Ticciati Msc in Finance.

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Substitution risk Rocco Letterelli Marco Ticciati Msc in Finance

Substitution 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 with Pre-settlement risk Conterparty risk

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

Substitution risk measurement: 2 questions: 1. If a counterparty was to default today, what would it cost to replace the derivatives transaction (i.e., what is the current exposure)? 2. 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)?

Substitution 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

Substitution 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

2 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

This 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

Substitution risk regulation… Regulation before the crises(basilea I and II) Regulation after the crises(basilea III)

Substitution risk According to basel I there are two approaches to estimate counterparty risk Basel II treated CCR loss as credit risk The second one accounts for substitution risk It is based on FPE(future potential expusure)CE(current expusureLEE(loan equivalent expusure)

Substitution 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

Substitution 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)

Substitution 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

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