## Two top tips for pricing

One of the most basic elements of any job on the trading floor is pricing.

This post gives you two important tips that can help you to:

• reduce the probability of making a pricing mistake,
• check that your pricing is reasonable,
• and generally get a better intuition for what current maket prices mean.

Neither tip is rocket science (by a long way!), but they can definitely spark a Eureka! moment, so they are worth passing on I reckon.

### Tip 1: price up the trades that will end up in your book

Suppose that you are pricing up a restructuring of a trade that was done previously. Let’s imagine that you have a client wishing to re-strike an older straddle to be at the money.

One natural way to do this is to price up the existing trade and say

‘it is worth X’

then price up the new trade and say

‘it is worth Y’

and then, after a moment’s thought, conclude that the client needs to pay Y-X for the restriking.

Did you have a moment of doubt:

“Is it Y-X or X-Y?”

#### You need a better scheme

For any trade with a number of components there is a good chance that you will add up and subtract things in the wrong order at the end of pricing the components. I suggest:

Top Tip 1: Price each component of the trade as if it will be a new component in your (trader’s) book, then all you need to do at the end is add the PVs (no subtracting at this point).

What this means is that you should describe each component of the trade as a long or short position, and include a plus or minus in the PV for each component: then add them all up at the end.

Effectively, this means we express a sum:

A + B – C – D + E,

as

A + B + (-C) + (-D) + E.

The key difference is that you can read this second version as saying that the trader will be:

1. long A,
2. long B,
3. short C,
4. short D,
5. long E,

So for the restrike example above, we should think of it as the two following components:

1. we buy a new straddle (with the same terms as the one we sold previously),
2. we sell a new straddle.

If they were new trades, each component would have a PV in the trader’s book of:

1. X
2. -Y

and it is now completely clear that the value of the trader’s portfolio after we have done this collection of trades will have increased by X-Y, so we would need to pay X-Y to the client in order for everything to add up to a PV of zero.

### Tip 2: prices are not intuitive, but rates are

If you tell me that that 5y5y 2% receiver costs 3% I’ll say ‘fine’.

But if I want to give some intuition to this price level I will convert it into an equivalent rate:

a PV 3% is equivalent to 5 years of annual coupons of about 65 basis points.

This is a powerful idea because it can be interpreted to mean that if I buy the 5y5y 2% receiver, then I will need the swap rate to be about 65 basis points in the money before my trade breaks even.

And once you have that interpretation, you can start to get a feel for the value of that trade: is 65 bps a lot to be paying or not?

My point is simple:

It is generally difficult to get an intuitive feel for prices.

It is however much easier to get an intuitive feel for rates.

Whenever I price up a structured swap trade I will use this trick:

Top tip 2: Convert all the price components into an equivalent coupon rate by dividing each PV by the PV01 of the swap.

For example, the price of a floored inflation note will be the price of the inflation leg minus the price of the floor (remember, this is the trade as expressed from the trader’s point of view, as it will be in his book afterwards), and if we express the floor premium as a rate we get a feel for how much of the coupon is being spent on the floor.

If we take the previous example of the component PVs being:

A + B + (-C) + (-D) + E,

then by dividing each by the PV01 of the trade we can convert these to rates to see how the final coupon is made up:

Coupon =

pay rate C,

pay rate D,