What determines the price of a credit derivative? There is a simple and obvious answer to this fundamental question: supply and demand. The main purpose of the realms of quantitative research and complicated mathematical calculations that surround any derivatives market is not to determine the price of these products. Its role is to make sense of the sometimes bewildering relationship between the price of different products and what the market believes the key assumptions are behind that price.
| Present value of spread = expected loss |
| Expected loss = probability of default*(1 - recovery rate) |
| Default probability = present value of spread/(1 - recovery rate) |
Of course, when firms agree to trade an innovative new kind of credit derivative – one with a different sort of pay-off structure, new features or unusual terms – quantitative research should help to educate the guesswork involved in pricing such a novelty.
Once a credit derivative has been traded – at the market price – the instrument needs to be valued periodically. Most banks, hedge funds and some insurance companies have to mark their positions to market. More fundamentally, companies need to value their positions to know whether they are sitting on a profit or a loss.
The best kind of valuation to use when valuing a position is a market valuation: how much would someone pay or charge to take on this risk today. For most standardised single name credit default swaps, indices, and index tranches, current market prices for standard maturities are available from third party sources, most notably the data provider Markit.
However, a market price for a standard maturity is not the same as a valuation for a trade done one year ago which now has four years to maturity. At the same time, some credit derivative trades are highly tailored and do not have prices from more than one dealer. So, just like in any over-the-counter derivative market, valuation often relies more on the theoretical than on actual market prices – although many inputs to the theoretical valuation are actual market levels.
Once a current price (theoretical or market) is determined, credit derivatives, like any financial contract, can be valued by discounting their future cashflows to the present day. The profit or loss is essentially the net present value of the difference between the contractual spread on the credit default swap and the current spread for a contract with the same maturity (an offsetting credit default swap).
Since the discount rate used for calculating net present value depends on the reference entity’s default risk, the higher the risk of default, the greater the probability that the two offsetting credit default swaps will terminate, reducing the present value of the future cashflows.
Therefore, any credit derivative valuation requires current prices to determine default rates. Many products similarly require inputs for credit correlation, recovery rates and volatility.