P2.T6.206. Counterparty risk (CVA)
206.1. Mary assigns to John a long position in an at-the-money (ATM) call option with a one year term and strike a price of $100.00. The current stock price is $100.00 with volatility of 60.0%. The risk-free rate is 3.0% with continuous compounding. N(d1) = 0.64 and N(d2) = 0.40. The present-valued expected exposure (EE) to the counterparty, who holds the short option position, is $23.00 with a probability of counterparty default of 5.0% and loss given default (LGD) of 75.0%. Which is nearest to John's payment for the long option position, if his cost includes a credit valuation adjustment (CVA)?
206.2. Sam prices a put option on an asset with the Black-Scholes-Merton option pricing model and calculates a model premium of $25.00. This $25.00 also coincidentally equals the present-valued expected exposure faced by Sam with respect to the short option position. Sam estimates the probability of counterparty default by the option writer to be 10% with loss given default of 40%, such that the expected loss = $25 EE(writer) * 10% PD * 40% LGD = $1.00. He concludes that the CVA-adjusted (net of counterparty risk) option price is $24.00. His colleague Jane observes that this calculation assumes no wrong-way risk. But there is a high, positive (+) correlation between underlying asset price and the credit quality of the option writer counterparty: both the counterparty and underlying share a sector that reacts to the same common factors such that adverse economic regimes depress sector asset prices while lowering sector credit quality (and increasing credit spreads). Is Jane correct that the CVA-adjusted option value deserves further adjustment?
- As the correlation is positive, this is instead right-way risk; but the true CVA-adjusted value remains $24.00 as there is no adjustment for right-way risk
- As the correlation is positive, this is instead right-way risk; therefore, the true CVA-adjusted value will be HIGHER than $24.00
- Jane is correct that this is wrong-way risk; therefore, true CVA-adjusted value will be LOWER than $24.00
- Jane is correct that this is wrong-way risk but expected loss is not impacted by correlation, so Sam correctly has the the CVA-adjusted value at $24.00
206.3. Acme Bank (A) is the floating-rate payer in an interest rate swap. Big Credit Corporation (B) is the counterparty who is the fixed-rate payer. Acme pays LIBOR in exchange for a fixed rate of 4.0% per annum. The credit valuation adjustment (CVA) to the mid-market value of the swap is given, per Canabarro, by CVA = E(A)*s(A) - E(B)*s(B); where E(A) is the present-valued expected exposure faced by Big Credit Corporation with respect to Acme Bank and s(A) is the risk-neutral loss rate of Acme Bank = PD(A) * LGD(A). From Acme Bank's perspective, the "net value" of the swap = credit-risk-free mid-market value + CVA. Consider three scenarios:
I. If the LIBOR curve increases, from Acme Bank's perspective, this will decreases the credit-risk-free value of the swap but will have zero effect on CVA
II. If Acme's credit spread increases, from Acme's perspective the net value of the swap (including CVA) will decrease
III. If Acme increases the quality of its collateral against the swap (i.e., lower collateral haircuts), from Acme's perspective the net value of the swap will increase
Which of the above is true?
- None are true
- Only I. is true
- II. and III. are true
- All are true