# Questions tagged [discounting]

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

I'd like this question to definitively guide a practitioner to using both $\mathbb{P}$ vs $\mathbb{Q}$ probabilities in trading and research. Let's take only one fact as given: if I have a risk-...
4k views

### Why do we discount in ois and not treasuries

OIS is the 1-day non-collateralized interbank interest rate. Such a rate is not risk-free. The market trades a very useful curve that is much closer to "risk-free": the government bond curve. So the ...
2k views

### Why are multiple custom curves (swap) built for one desk?

Currently in a journey of learning and getting my hands a bit dirty with Interest Rate Swaps. Why there are multiple customized curves built by many even within one desk? For e.g. Short Rates desk ...
278 views

### Discount curve and payment frequency

In case of uncollateralised trades, where we use LIBOR rates for discounting, does the LIBOR tenor have to match with the payment frequency? For example, one of the swap leg pays USD floating amount ...
366 views

### Risk-neutral expectation equation with collateral and funding costs

I am looking at a paper by V. Piterbarg, Funding beyond discounting: collateral agreements and derivatives pricing, that you can download on the following link, in which the author adapts the Black-...
2k views

### Cheapest-to-deliver (CTD) discount curve

Can someone explain, in layman's terms, the mechanics (the algorithm steps) of the construction of the discount curve in the case when the CSA allows the posting party to choose a currency (from a ...
202 views

### Calculating the Discount Margin for a FRN

I am working with a programming case where there are two methods of calculating YTM / discount margin for bonds and FRNs. Both methods use an iterative approach to find a rate / spread that ...
4k views

### What exactly is the OIS Black VOL?

While poking around in Bloomberg I stumbled upon the following data set: EUR SWPT BVOL OIS for various maturities. Obviously OIS must suggest OIS-discounting but how is it related to the Black-...
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### Proof that we can price any derivative as the discounted value of its expected return under the risk neutral measure

I am reading a paper which tries to convey the intuition behind the Black-Scholes pricing formula. In that paper, the author states the following two things without proof, and I would like to know why ...
124 views

### Correct Discount Curve for Exchange Traded (Centrally Cleared) Products

What's the correct discount curve to use for exchange traded products? Would these be discounted at the OIS rate (because of the central clearing house)? E.g. the E-Mini S&P500 Future @ CME: I'm ...
262 views

### Bootstrap ESTER and SOFR curves with Quantlib Python

Is it possible to bootstrap the new ESTER and SOFR term structures in Quantlib? More in general, does the process work as the usual one? Given these are simple indices that are published on a daily ...
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### Discount rate in IRS valuation

This might be a very basic question but I didn't find the answer in the materials I saw on Google. What is the interest rate used to compute the discounted cash flows for both the fixed and variable ...
60 views

### What is time 0 price of Libor starting t for the period $t$ to $t+\delta t$

I was asked this in an interview. The correct answer, I was told, follow from this argument Let $L_0[0,t]$ denote the time 0 price of Libor for period $0$ to $t$. Let $L_0[t,t+\delta_t]$ denote the ...
363 views

### Discount factor taking into account yield curve shape

I have always been told that the discount factor formula is just: $$DF(T) = \frac{1}{(1+L_{t_0})^T}$$ where $L_{t_0}$ is the LIBOR rate on one period (the first one I guess) and $T$ the number of ...
56 views

### Can I use these rates for ACT/360 discounting?

I have calculated forward rates like this: $r_{t_1,t_2} = \left(\frac{(1+r_2)^{d_2}}{(1+r_1)^{d_1}}\right)^{\frac{1}{d_2-d_1}} - 1$ I want to find the discount factors for these forward, with ACT/...
169 views

### Bond discounting conventions

during the preparation for my thesis, I've come across some strange discrepancies between literature and the information I've been taught. It comes down to the proper way of discounting cash-flows of ...
175 views

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

Consider a cash flow stream of a single payment (1 period away). Its net present value is typically presented as $$\text{NPV} = {\text{EV}(\text{Cash Flow}) \over 1 + d} \tag{1}$$ Here $d$ is ...
72 views

### Arbitrage when discounting and forward computation is done with different curves

I notice that (equity derivatives) trades generally are priced with different forward curve and discounting curve, which clearly lead to arbitrage. Is this arbitrage value too small to be ignored? How ...
396 views

### ESTER replacement for EONIA/EURIBOR

Does anybody know what impact the replacement of EONIA with ESTER ( Euro Short TErm Rate ) will have on discounting existing or new derivatives once EONIA will be restricted as of Jan 2020? I'm ...
5k views

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

I am trying to understand the currency basis calculation and whether there is a difference in currency basis when quoted vs. OIS and -IBOR rates.
141 views

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

I am reading Options, Futures, and other derivatives by John C. Hull. In the chapter on Binomial trees, he remarks: A risk-neutral world has two features that simplify the pricing of derivatives: ...
223 views

### Characteristics of a Discount Curve

Does the discount curve used for discounting cash flows have to be a zero coupon, annual compounding, actual by actual day basis curve? In practice, does a curve used for discounting necessarily have ...
864 views

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

Within the IFRS9 framework it is stated that one needs to determine the expected losses and discount these with the effective interest rate (EIR), i.e. the contractual rate at initiation. However, I ...
65 views

### Discounting in multicurve environment

Given that the longest tenor for LIBOR in 12M, what rate do we use to discount a cash flow due in, say, 18 months? Some suggest that we use the 12M rates for 1 year and 2 year to interpolate, but ...
48 views

### Continuously Compounded rate less than a discretely compounded rate [closed]

I'm looking at an example in a well known book and its saying "consider an interest rate that is quoted as 10% per annum with semi annual compounding" The book puts 10% as the semi-annual rate, ...
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### Macaulay's Duration with Zero Rates

The definition of Macaulay's Duration is the weighted average maturity of cash flows and is calculated as- $$D_{mac}=\frac{\sum_ttPV(C_t)}{V}$$ where $PV(C_t)$ is the present value of the cash flow ...
129 views

I am confused as 2 methods give different answers. The difference lies in the "to the power" numbers for discounting. Example: 2 year semi annual bond (4 periods), $1m annual Coupon Payment, 5% Yield ... 1answer 2k views ### What is the proper discounting of PIK and non-compounding bullet loans? This question pertains to two types of loans. Pay-in-kind (PIK) and bullet loans with quarterly payments. 1. PIK Loans A PIK loan is a loan where periodic interest is NOT paid, but added to the ... 2answers 59 views ### Discounting for XVA I was thinking that since CVA is on uncollaterized exposure, we should be using USD-0/LIBOR discounting environment. But I observed that the industry uses CSA discounting for CVA/uFVA computation. Am ... 0answers 76 views ### discount factor, zero rates, zero curve from BBG How can I calculate the discount factor for row 1? I would do $$\frac{1}{(1+ 2.13763/100)^{(90/360)}} = 0.994726197703956$$ My ultimate goal is to reproduce the Zero Rates. Any hints welcome. ... 0answers 40 views ### Discounted Costs [closed] Suppose we were given a discounted cost of £12,956. This was generated using a discount factor of 3.5% and a time-horizon of 45 years. Is it possible to obtain what the non-discounted cost is today?... 0answers 47 views ### Discounted self-financing portfolio still a self-financing portfolio? Assume a self-financing portfolio$V_{t}=\theta_{t}^{0}S_{t}^{0}+\theta_{t}S_{t}$with$S_{t}^{0}$the value of the non-risky asset at time$t$and$\theta_{t}^{0}$the amount of shares of the non-... 0answers 111 views ### Why don't we build the discounting curve and projection curve from bonds We know that we always build the discounting curve and projection curve from money market instruments, index Futures, interest rate swap and OIS Libor swap (depends on the period). But why don't we ... 0answers 23 views ### Source for derivation of acquisition price for given IRR and cash flows Does anyone know a quotable source - book/academic or practitioner's paper - that derives the acquisiton price for a target firm when the buyer's desired IRR and all cash flows over time of the target ... 0answers 35 views ### Monthly Discount Rate in NPV Calculation [closed] I have been offered 2 payment methods as I was buying some tools for a company I work for. I need your help to assess the best method. Here it goes, Total cost is$100 and I don't want to pay it all ...
WACC in my mind is effectively a post-tax measure: $$\text{WACC} = \frac{E}{V} k_e+\frac{D}{V}k_d(1-t)$$ In this case should cash-flows, in particular loan cash-flows be adjusted for tax as well? ...