18 votes

$\mathbb{P}$ vs $\mathbb{Q}$ Probabilities - Transitioning Between Measures

$\mathbb{P}$ is the true probability measure. Measure $\mathbb{Q}$ is a measure of convenience that allows risk neutral pricing. Stochastic discount factor $M$ takes you between the two. If you care ...
Matthew Gunn's user avatar
  • 6,944
13 votes

Why do we discount in ois and not treasuries

There are two parts to this question: 1) Is OIS a good risk-free proxy? and 2) Why is OIS used to discount cash flows of derivatives. First, overnight indexed swaps, in the US, are indexed to the Fed ...
Helin's user avatar
  • 11.7k
10 votes
Accepted

Cheapest-to-deliver (CTD) discount curve

Collateral posted in currency XYZ is remunerated at $\text{OIS}_{\text{XYZ}}$, which translates, using the XYZUSD basis, into a synthetic USD rate $\text{OIS}_{\text{USD}}^{\text{XYZ}} = \text{OIS}_{\...
Antoine Conze's user avatar
8 votes
Accepted

Risk-neutral expectation equation with collateral and funding costs

One derivation is to replace $V_u$ in Equation $(5)$ using the expression given by Equation $(3)$ and then work out to reach $(5)$; see Appendix A in this paper for more details. Here, we provide ...
Gordon's user avatar
  • 21.1k
7 votes
Accepted

Trading desk assumes zero percent discount rate?

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 ...
Dimitri Vulis's user avatar
6 votes

Discount curve and payment frequency

Better yet, don't use LIBOR for discounting at all. Since LIBOR involves credit spread over the risk free rate, using LIBOR for discounting would adjust the deal's market value to reflect some amount ...
Adam N.'s user avatar
  • 61
6 votes
Accepted

If I have the present value of an amortizing bond's cashflows, how do I figure out price?

Bullet bond prices are quoted as a percentage of face value (par). For most amortizing bonds that have already amortized part of the initial principal (face value), the price is a percentage of the ...
Dimitri Vulis's user avatar
6 votes

Market convention for building the front-end of the SOFR discounting curve

The front end of the SOFR curve has a lot of structure in it. I cant talk to "market convention" as I doubt something like that exists yet but I use Fixed for floating SOFR swaps (1w, 2w, ...
river_rat's user avatar
  • 980
6 votes

Delta of Black formula vs numerical

Your Delta_fd is forward delta (you're bumping the fwd). Delta is spot delta. Hence the discount factor.
user35980's user avatar
  • 1,386
5 votes

Discounting Curve in Quantlib/Python

You can use the DiscountCurve class, that takes a list of dates and a list of corresponding discount factors. The one exported by default in the Python module uses ...
Luigi Ballabio's user avatar
5 votes

Trading desk assumes zero percent discount rate?

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 ...
demully's user avatar
  • 5,061
5 votes

Future Value: the functions in Excel, Matlab and Numpy Financial don't work when the number of periods is large

This is not a bug, just how computers work. Would have been better to ask in a non finance forum though. It is called (Integer) Overflow. If you are into reading humorous chats, you can have a look ...
AKdemy's user avatar
  • 8,739
4 votes

Does the traditional NPV formula of a cashflow double count risk?

That formula is algebraically equivalent to saying different, stochastic assets can have different expected returns. $$ \mathbb{E} \left[ R_i \right] = r_f + \gamma_i $$ Some simple algebra Let $...
Matthew Gunn's user avatar
  • 6,944
4 votes
Accepted

Bond discounting conventions

You are basically just arguing semantics from two models, neither of which are necessarily precisely accurate. If you observe the assumptions regarding yield to maturity, you have; 1) Coupons can be ...
Attack68's user avatar
  • 10.2k
4 votes
Accepted

Why use the risk-free rate for discounting in a risk neutral world?

The first statement is kind of clear. If all investors are risk-neutral, they simply do not care about risk and do not pay more or less regardless how risky an asset is. As a consequence, the return ...
Kevin's user avatar
  • 15.9k
4 votes
Accepted

Proof that we can price any derivative as the discounted value of its expected return under the risk neutral measure

This holds due to a change of measure. There is the real-world $\mathbb{P}$ and the risk-neutral world $\mathbb{Q}$. (I am going to assume constant interest rate $r$) The first fundamental theorem of ...
Kevin's user avatar
  • 15.9k
4 votes

Find out the effective monthly discount rate for a 10% annual discount rate

I think that what you want is to convert an annually compounded interest rate to a monthly compounded interest rate, right? $$\left(1+\frac{r_{monthly}}{12}\right)^{12} = (1 + r_{annual})$$ $$r_{...
David Duarte's user avatar
  • 5,815
4 votes
Accepted

What is the standard risk free rate used to discount options?

Since pretty much all trades (at least interbank) are collateralized nowadays, you would follow the principle of CSA discounting and use the interest rate on the collateral as a discount rate. ...
Adam N.'s user avatar
  • 56
4 votes

Future Value: the functions in Excel, Matlab and Numpy Financial don't work when the number of periods is large

The computer programs are evaluating the following expression: $FV(i,N,PMT,PV)=-PMT[\frac{(1+i)^N-1}{i}]-PV(1+i)^N$ the test case you are running is the special case where you choose $PMT=-i\cdot PV$ ...
nbbo2's user avatar
  • 11.3k
4 votes
Accepted

Delta of Black formula vs numerical

I think I disagree here. FD delta should yield a value that is very close to $exp^{-rT} * N(d1).$ If not, I think you may use a non-conventional implementation of Black-76. Also, you wrote that your ...
AKdemy's user avatar
  • 8,739
3 votes
Accepted

Bloomberg terminal swap zero curve calculation

It looks like you should use a different convention for the zero rates. I tried the following: $$\left(1+r_{0;t_{0}}\frac{t_{0}}{360}\right) \times \left(1+r_{t_{0};t_{0}+t{u}}\frac{t_{u}}{360}\right)...
Olaf's user avatar
  • 1,909
3 votes

Dual discounted forward curve

Which currency are you looking at ? Say that your 1y swap would have yearly fixed payments vs 3M floating payments. Your 1.5y swap would probably have: a fixed payment 6m after effective date and ...
Bozothegrey's user avatar
3 votes

When to use what discount rate?

Ideally, you would discount a certain cash flow by its appropriate curve. For example: 1) you would discount the cash flow of your fixed income investments by the yield curve of the Treasury market;...
python_enthusiast's user avatar
3 votes

What is the EUR swap curve on Bloomberg? I.e. what is the EUR equivalent of S23 curve on Bloomberg?

The curve Bloomberg EUR swaps curve (YCSW0045 Index) is indeed the euro equivalent of the Bloomberg USD swaps curve (YCSW0023 Index). By equivalent I mean that each curves are constructed in the same ...
Olórin's user avatar
  • 1,223
3 votes

For IFRS9, losses should be discounted with the EIR, why is that sensible?

1. $V_0$ is what the bank would write for it's book value This is only the case for items held on the balance sheet at Fair Value. Most banks will hold many assets/loans at amortized cost (principal ...
Trevor Hansen's user avatar
3 votes
Accepted

ESTER replacement for EONIA/EURIBOR

I believe that Eonia can still be used for discounting derivatives after 2020. Article: https://www.risk.net/derivatives/5848051/esma-eonia-can-be-used-in-csas-after-2020 If it becomes illiquid, ...
dm63's user avatar
  • 17.1k
3 votes
Accepted

Recommended Instruments (and sources) for Constructing Money Market Yield Curves

A plethora of instruments, a menagerie of curves Different instruments are traded in different ways, and relate to a collection of curves. Floating rate instruments depend on some index in order to ...
Phil H's user avatar
  • 3,669
3 votes
Accepted

What is the difference between a cleared interest rate swap and a OTC interest rate swap with collateral in theory

For both cleared and OTC swaps you need to post margin. If you are delivering cash then you will receive OIS in generally in either case. As OTC trades are bespoke you might have a different ...
JoshK's user avatar
  • 2,613
3 votes

Calculating the Discount Margin for a FRN

There are two types of discounting approaches of a future payment in your question. Zero rates and forward rates. Let's just briefly consider each in turn. i) ZERO RATES. The zero rate discount ...
Dom's user avatar
  • 2,147
3 votes
Accepted

Arbitrage when discounting and forward computation is done with different curves

The last edition (10th, 2017) of Hull's book explains it fairly well. Basically, there is indeed a theoretical arbitrage within the dual curve framework: you could borrow at the overnight rate (Fed ...
siou0107's user avatar
  • 2,680

Only top scored, non community-wiki answers of a minimum length are eligible