This post may appear to be something of a diversion from our central topic of credit options, but it is one that I have realised we cannot avoid. You can pick up the context of the blog from our previous posts
Setting the scene
Suppose we were trying to calculate the profit or loss on a long equity call option. We would calculate this using the following expression:
MAX (underlying price – strike, 0) minus premium paid.
Consider how this might look for a credit option If we are long a payer option with a strike at 100bps and the underlying index is trading at 120bps then the contract is 20 basis points in the money. But think about this – if the underlying index has a maturity of 5 years, then the investor earns a 20 bps annuity over the entire life of the underlying index if they were to exercise the option.
Introducing the PV01
What is the equivalent of this in terms of a single cash amount payable right now? Logically we would need to present value to take account of the time value of money (perhaps using swap rates). But we need to also to consider whether the underlying asset will experience any defaults over its maturity.
Definiting PV01 for credit options
This introduces the concept of PV01. We can define the concept as: “today’s monetary value of receiving 1 bp per year for the life of the contract, which is either maturity or default, whichever occurs first.” Another popular term to describe the concept is a risky annuity.
Survival probabilities
In simple terms suppose that we are due to receive a single dollar unit of cash in exactly one year’s time. Interest rates are 5% and if we assume that there is an element of associated credit risk, we will assume that there is an arbitrary 3% chance of default. Default is binary – you default or survive and so we could argue that there is a 97% chance of surviving. So our PV01 is:
= $1 * 0.9524 * 0.97
[The 0.9524 is (1/1+5%)]
= $0.9238
That is, receiving a credit risky dollar in 12 months’ time is equivalent to receiving $0.9238 today. If you were to extend the logic out for a five year CDS index, then you would end up with a value of just less then ‘5’. So if we take an arbitrary value of 4.75 for the PV01 of a 5 year CDS what does this mean? When we take into account interest rates and survival probabilities, receiving a 1 unit cash flow per annum is equivalent to receiving 4.75 units upfront.
Unit of measurement
What can be confusing is that some of the literature expresses the measure without units. The easiest way to think about it is: what is the PV01 of receiving 1 bp pa over a given period? If we use the previous values it would be equivalent to receiving 4.75 bps upfront.
So let us return to the profit and loss equation on a payer credit option. We can now write this as:
MAX (underlying price – strike, 0) * PV01
So using the values earlier in this note and the arbitrary PV01 value shown above we get:
= MAX (120 – 100, 0) * 4.75
= 20 *4.75 = 95 basis points
So the intrinsic value of the option is 20 bps per annum over the life of the deal which is equivalent to a single upfront value of 95 basis points. If the upfront premium was 35 bps, then the net profit is 60 bps, which on a notional of 10m would be 60,000.
PV01 is not DV01
Just to say that the PV01 is not shown on most professional trading systems but can be inferred from the upfront adjustment. What is shown is the DV01; this is the amount by which the present value will CHANGE as a result of in the CDS spread. That is a different concept.