When Zero-Rate Discounting Is Acceptable in Option Models

# Trading desk assumes zero percent discount rate?


# Trading desk assumes zero percent discount rate?












All the swaption and option models I have encountered at my employer's trading desks have assumed a zero percent discount rate. I have proposed using the LIBOR curve, but management responded that "we are not a bank", and they said "using a yield curve adds unnecessary volatility to the model", when I instead proposed using the US yield curve. Does this seem odd or troubling to anyone else?

## Answer by Dimitri Vulis (score 7, accepted)

https://quant.stackexchange.com/a/60098

If they were a bank, or insurer, utility etc, then some regulator would likely encourage them do everything that others do, whether they like it or not, or whether it makes any sense. But if no regulator tells them to... and if if they don't have exposure to interest rates beyond 1 year...

well, let's look at USD 1 year swap rate, for example, https://fred.stlouisfed.org/series/ICERATES1100USD1Y

and 1y treasury https://fred.stlouisfed.org/series/DTB1YR

Moreover the Fed has promised near-0 fed funds for the next few years. https://www.cnbc.com/2020/04/29/fed-decision-fed-pledges-to-keep-rates-near-zero-until-full-employment-inflation-come-back.html

just as they did a back here https://www.nytimes.com/2011/08/10/business/economy/fed-to-hold-rates-exceptionally-low-through-mid-2013.html

I actually knew one buy-side shop that in some of their models effectively took a view that USD rates were 0. Whether it's OK depends on the interest rate sensitivities - in some situations, assuming that 1.5% is 0 is close enough, and in others it is not. That was good enough for them from about 2008 to 2017; then the models did not work so well starting late 2017 (no immediate P&L impact, just the model results were clearly no good and needed manual overrides), and now the rates are back down where this assumption might have been OK again in their example, except now they've incorporated interest rates better into their models.

So to address your question - does it seem odd - yes, a little odd, especially if they were still doing it while the rates were further from 0 (2018-2019) than they had been in prior years. But not necessarily unheard of or troubling - not red-handed evidence of Madoff-like malfeasance, just someone's business decision, probably too risky for my personal tastes. :)

A good control would be to estimate periodically some kind of firm-level sensitivity to a (totally unexpected at this point) 1970s-style sharp rise in the interest rates, like 3% up - see what will break, and have all contingency plans in place. Like, the ability to flip a switch and start using well-tested and ready to go models that do use interest rates.

## Answer by demully (score 5)

https://quant.stackexchange.com/a/60117

In a past life, I was an equity strategist at a sell-side bulge bracket firm. In 2008 (obviously) the bank decided to take a long hard look at the funding costs of its derivatives books. So they appointed an MD in IBD/corporate finance who would obviously lack “skin in that game”, and I was his chosen “research guy” (deliberately not then from a fixed income background). Of course, the idea that risk positions supported by the bank’s balance sheet had ANY funding cost, even if the bank’s balance sheet did, was pretty much heresy to every Rates and FX trading desk. We were top3 FX broker globally at the time; and told we should exit the FX business if the balance sheet use was in any way chargeable!

So I absolutely sympathise with your situation!

In our situation, we simply told the traders that balance sheet had become a scarce resource, so there was a cost of capital due from them to the bank for their BS utilisation. The IBD bigwig then reminded them that if they disagreed, and felt so aggrieved they threatened to quit and join a hedgie, the hedgie would charge them more than us; plus they would lose access to visibility over their vaunted flows...

Wargaming this negotiation, we soon realised that discounting all positions was a dud proposition. We would be discounting all of our losing positions, so the bank could actually end up worse off discounting! If our traders lost money, then our “NPV” would be lower than our actual future losses, that would have to honoured in full. So discounting every position’s NPV doesn’t actually help...

So there’s a very real difference putting a positive price on the risk of any and all positions versus trying to discount their expected future value all to a “fair” NPV.

This might or might not be relevant to your dilemma. I don’t know. But said in case it is in any way helpful. Happy to discuss further if you feel confident.

All the best, DEM

## Answer by Attack68 (score 2)

https://quant.stackexchange.com/a/60150

I would add to the answers here, the concept of margin of error.

If your swaptions and options are short dated the effect of discounting them is going to be minimal, for a one year option at 1% OIS you have a 0.99 discount factor, i.e a 1% error in valuation if you substitute a discount factor at 1.00 and ignore discounting. If your models are similarly simple it may be that they have a larger tolerance to the more accurate dealer prices anyway, say 2-6% error.

In the latter case correcting a 1% error does not materially improve a 5% initial error, given the necessary implementation work and alterations to risk reporting.

So, in conclusion, it may not bother me or it might be imperative to change, its all completely context dependent.