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# P2.T6.914. Pricing counterparty risk with the credit value adjustment (CVA) (Gregory Ch.14)

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Learning objectives: Explain the motivation for and the challenges of pricing counterparty risk. Describe credit value adjustment (CVA). Calculate CVA and the CVA spread with no wrong-way risk, netting, or collateralization.

Questions:

914.1. Your colleague has drafted guidance for your firm's computation of the credit value adjustment (CVA). The guidance begins with four principles: risk-neutrality, discounting, proportionality, and inseparability. The principles are summarized as follows:

I. Risk-neutrality: CVA can be computed either with risk-neutral (aka, market-implied) or real-world (aka, historical) parameters
II. Discounting: CVA should be discounted to present value, either via discounted expected exposure (EE) or via explicit discount factors
III. Proportionality: CVA will be proportional to the likelihood of default (PD), the exposure (EE) and the percentage amount lost in default (LGD).
IV. Inseparability: It should be impossible to separate the valuation of a transaction from its counterparty risk as measured by CVA

Each of the principles is valid, EXCEPT which of the principles is INCORRECT?

a. Risk-neutrality
b. Discounting
c. Proportionality
d. Inseparability

914.2. Your colleague Robert was tasked by the firm's Chief Risk Officer (CRO) to estimate the credit value adjustment (CVA) charge on a derivative exposure. He was asked to perform a quick calculation and told therefore that a rough approximation is acceptable. His only facts include the following:
• A simplistic assumption that expected exposure (EE) is constant at 5.0% of notional
• Therefore, the expected positive exposure (EPE) is also 5.0% of notional
• A credit spread of 400 basis points
• Recover rate of 50.0%
• Constant hazard rate of 6.7%
• Approximate maturity of 5.0 years
Which of the following is nearest to Robert's correct estimate of the credit value adjustment (CVA) charge?

a. About 20.0 bps per annum
b. About 33.3 bps per annum
c. About 50.0 bps per annum
d. Robert cannot estimate the CVA charge because the market risk component information is missing

914.3. The Chief Risk Officer (CRO) at Global Financial Corporation has requested that his staff price the counterparty risk of a 3-year derivative exposure to a major counterparty. His staff assumes that the counterparty’s default probability follows a constant hazard rate process. Below are the forecast data with respect to the expected exposure, the CDS spread and the anticipated recovery rates:

Further, the analysis will employ the following assumptions:
• A credit support annex (CSA) cover this exposure and requires collateral posting of USD $10.0 million. • The current risk-free rate of interest is 4.0% per annum with continuous compounding and the term structure of interest rates is presumed to remain flat • Collateral and exposure values will remain stable as projected over the 3-year life of the contract Which of the following is nearest to the credit value adjustment (CVA) for this position? a.$300,000
b. $625,000 c.$1.0 million
d. \$2.7 million