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### how exactly do traders determine prices

Posted: **January 20th, 2020, 11:45 pm**

by **billyx524**

Hi,

I have a question on how exactly do traders determine their price quotes. let's say a clients comes to the trader, and asks for a price on an exotic instrument. the trader goes to his quant, and asks for a theoretical/model price. but then how does the trader determine what final price to give to the client? what spread above the model price will he charge?

### Re: how exactly do traders determine prices

Posted: **January 21st, 2020, 6:37 am**

by **frolloos**

This is hard to answer in full generality. It will depend on the type of exotic, if there is already a natural approximate offset to the risks of the exotic on the existing book or whether it will need to hedged, and if so how simulations of the hedge error depend on the model parameters used to hedge, on the tenor of the instrument, the hedge instruments and so forth.

### Re: how exactly do traders determine prices

Posted: **January 21st, 2020, 6:44 am**

by **billyx524**

let's say for a bermudan swaption priced under hull-white model. what would be the difference between the quote price given to the client and the model's theoretical price?

### Re: how exactly do traders determine prices

Posted: **January 21st, 2020, 12:08 pm**

by **frolloos**

Sorry I don't have sufficient IRD experience to give you a sound answer - maybe others can help you. My background is more EQD, and specifically var/vol swaps.

And actually, I doubt whether the market uses HW1F to price / hedge Bermudan swaptions, but I may be wrong.

### Re: how exactly do traders determine prices

Posted: **January 22nd, 2020, 11:59 am**

by **lePiddu**

Frolloos is totally right: the final price depends on many factors. I would also add that it depends also on the "internal rules" of the bank: for some trades you cannot charge more than x times the Vega + y times the Delta of an option. This is especially true when the instrument is part of some structured note (e.g. bermudan swaptions to cancel the swap used to hedge IR risk of callable bonds): in this case the bond may have a maximum retail price and therefore the hedge has some kind of "profits cap".

On a side note: yes, HW1F is still used to price bermudans. You are "disregarding" higher order yield curve movements (like steepening-flattening) but in some markets (EUR for example), two-factors short rates models sort of "collapse" in one-factors short rate models (you end up with rho=1), therefore HW1F is still "good". As for the smile, you can easily calibrate the model on the exact strike of the bermudan you are pricing (instead of ATM swaptions), and of course hedge using those strikes instead of ATM.

As always "good" depends on what you are actually up to =).

### Re: how exactly do traders determine prices

Posted: **January 22nd, 2020, 1:42 pm**

by **tw**

Frolloos is totally right: the final price depends on many factors. I would also add that it depends also on the "internal rules" of the bank: for some trades you cannot charge more than x times the Vega + y times the Delta of an option. This is especially true when the instrument is part of some structured note (e.g. bermudan swaptions to cancel the swap used to hedge IR risk of callable bonds): in this case the bond may have a maximum retail price and therefore the hedge has some kind of "profits cap".

On a side note: yes, HW1F is still used to price bermudans. You are "disregarding" higher order yield curve movements (like steepening-flattening) but in some markets (EUR for example), two-factors short rates models sort of "collapse" in one-factors short rate models (you end up with rho=1), therefore HW1F is still "good". As for the smile, you can easily calibrate the model on the exact strike of the bermudan you are pricing (instead of ATM swaptions), and of course hedge using those strikes instead of ATM.

As always "good" depends on what you are actually up to =).

I would have said the crucial aspect is how much competition for the trade there is.

People will charge what they can get away with, but usually it is something of a competitive process.

The more subtle question is the mechanics of what price is used to generate collateral/margining calcs.

### Re: how exactly do traders determine prices

Posted: **January 22nd, 2020, 4:56 pm**

by **lePiddu**

Totally agree with tw, competition is crucial. Althougha as far as I know, EUR market for Bermudan is not too wide, I always match with the same 3 or 4 counterparties.

As for collateral (again as far as I know) bermudans are all bilateral, therefore we both report our MTM to each other and start "litigations" only when there's a substantial difference ( > 15% of the Delta sensitivity as I recall). So we agree on MTM not on models. Litigations may end up requiring a third party to compute the MTM but I've never end up that far.

### Re: how exactly do traders determine prices

Posted: **January 22nd, 2020, 5:20 pm**

by **frolloos**

@lePiddu - thanks for the colour, I wasn't aware that HW1F is used for bermuda swaptions, good to know.

Good point on competition, which is another factor to take into account, and can distort the 'true' model price. I have seen trades (in eqd) where some parties try to initially buy themselves into a trade with the expectation that they can roll the trade with the same counterparty and in the long term gain from it.

In any case, for the OP should be clear that there is no straightforward answer. But, billyx524, if you happen to be a practitioner at the buy-side, there is a very easy way to find out the b/a and hence a sense of the 'true' mid-price for the instrument you are curious about: ask 3 banks to give you indics. If you happen to be at the sell-side, well probably your colleagues can give you the answer.

### Re: how exactly do traders determine prices

Posted: **January 22nd, 2020, 6:08 pm**

by **tw**

Totally agree with tw, competition is crucial. Althougha as far as I know, EUR market for Bermudan is not too wide, I always match with the same 3 or 4 counterparties.

As for collateral (again as far as I know) bermudans are all bilateral, therefore we both report our MTM to each other and start "litigations" only when there's a substantial difference ( > 15% of the Delta sensitivity as I recall). So we agree on MTM not on models. Litigations may end up requiring a third party to compute the MTM but I've never end up that far.

It is the reporting the MTM bit that always for a bit of cynical amusement...

The number of times (in illiquid instruments) I've seen both counterparts mark positive day one MTM, or it kicks of a massive argument in

terms of gouging accusations, or creates a lot of hurt pride and bad sales relationships.

The (best kept nameless) US bank I worked for had a way of "amortizing" day one P&L for client biz.

But this was in the pre-crash era....