Questions tagged [discounting]

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8
votes
1answer
472 views

$\mathbb{P}$ 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-...
5
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3answers
3k 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 ...
5
votes
1answer
237 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 ...
5
votes
1answer
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 ...
4
votes
1answer
329 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-...
4
votes
1answer
1k 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 ...
4
votes
1answer
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-...
4
votes
1answer
89 views

Discounted asset price is martingale in BS model

I want to verify that the discounted stock price process $\mathrm{e}^{-r(T-t)}V(S_t,t)$ is a martingale in the BS-model. Using Ito's formula and the BS-PDE I get that $$ \mathrm{d}\mathrm{e}^{-r(T-t)}...
3
votes
3answers
880 views

Two different ways of pricing that leads to two answers

This question might appear trivial to many (considering the questions on this site), but I think it reflects something fundamental that I am missing. To keep things simple, assume everyone is risk-...
3
votes
2answers
178 views

expected change in value of a derivative in a multicurve framework

I'm reading Piterbarg paper, "Funding beyond discounting: collateral agreements and derivatives pricing." and have a question about equation $(6)$. There he says that for a derivative we have $$E_t[...
3
votes
0answers
582 views

Properties of Geometric Brownian Motion Integrated w.r.t. Time (i.e., distribution of a Yor Process)

Let $S_t$ be a process which follows a Geometric Brownian Motion: $\frac{dS_\tau}{S_\tau} = \mu \,d\tau + \sigma \,dW_\tau$ By Ito's lemma, we have: $S_T = S_t e^{(\mu-{\sigma^2 \over 2})(T-t) + \...
2
votes
1answer
2k views

Discounting Curve in Quantlib/Python

I'm using Python 2.7.12 with the QuantLib package. I'm trying to price fixed bonds. I understand how to create a bond object. How to get the "right" discounting curve is kind of a problem. Assuming a ...
2
votes
1answer
238 views

Dual discounted forward curve

I was wondering how to calculate the forward rates based on OIS discounting for the half year terms. I know how to do this for the full year terms -> just making sure that the two legs are equal to ...
2
votes
2answers
192 views

Is an options implied dividends DCF model consistent with risk neutral/arbitrage-free valuation?

We're talking about how we price every financial instrument: by discounting the payoff, that is, we take future cash flows and we discount them by a proper rate which takes into account the risk of ...
2
votes
1answer
3k views

Z-Spread vs Discount Margin

I'm comparing two types of discounting: Z-Spread and Discount Margin. Reading the article by O'Kane Credit Spread Explained I found Z-Spread is used for fixed rate notes meanwhile Discount Margin, ...
2
votes
1answer
1k views

Which discount curve to use when valuing multi currency swaps

I've been looking around the internet but cannot find the exact answer to my question. Normally when valuing an IRS one uses eonia (for eur swaps) to discount the cashflows. Let's imagine I have a ...
2
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0answers
138 views

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 ...
2
votes
1answer
56 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 ...
2
votes
1answer
338 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 ...
2
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0answers
53 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/...
1
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1answer
151 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 ...
1
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3answers
142 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 ...
1
vote
1answer
253 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 ...
1
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2answers
3k 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.
1
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1answer
180 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 ...
1
vote
1answer
628 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 ...
1
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1answer
39 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, ...
1
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1answer
84 views

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 ...
1
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1answer
159 views

Discount factor

Suppose we have : $r$ - zero coupon rate, constant over time, $n$ - a number of years (an integer), $\theta$ - a fraction of a year $(\theta < 1)$ , calculated with the relevant day count ...
1
vote
2answers
124 views

Why to 2 methods to calculate bond price with semi annual return give different answers?

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 ...
1
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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 ...
1
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0answers
31 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: ...
1
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0answers
44 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-...
1
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0answers
56 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 ...
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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 ...
1
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0answers
27 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 ...
1
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0answers
32 views

Calibration of stock's intrinsic value under the gordon model

Assume we have the constant growth Gordon model, for a stock paying dividend $D$,Earnings per Share $EPS$, annual growth rate $g=ROE*(1-\frac{D}{EPS})$ and discount rate $r$. Then: $IV=\frac{D*(1+g)}...
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0answers
67 views

Is the discount rate the same for all market participants?

When determining what to pay for a company or asset people typically discount the future cashflows by the cost of equity, which is defined as the 'risk free rate' ...
1
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0answers
51 views

Should cash-flows discounted at WACC be pre- or post-tax?

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? ...
0
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1answer
144 views

When to use what discount rate?

By discount curve $D(t)$ I mean the discount rate applied to a cash payment or receipt at time $t$. What is the correct terminology to use? I have seen the term "yield curve" thrown around, but I'm ...
0
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2answers
91 views

Calculation VaR on long term period

I'm calculating VaR numbers from historical data for a single instrument (it's plain vanilla, not a derivative) and receive such variables: I could provide necessary data, and formulas but I guess ...
0
votes
2answers
140 views

Does a 1Y swap depend on zero curve beyond the 1Y point?

When using market swap rates to calibrate a discount curve, it seems that the PV of a 1Y swap depends on the zero curve at points beyond the 1Y mark. For example, a USD 1Y swap with trade date today (...
0
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1answer
67 views

In DCF, why is the discount rate interpreted as the minimum rate of return?

Is there an intuitive explanation of why, in DCF modeling, the discount rate should be interpreted as the minimum rate of return? This doesn't make sense to me because I think of the NPV as "what all ...
0
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1answer
2k views

Bloomberg terminal swap zero curve calculation

I would like to ask about swap zero curve calculation algorithm by Bloomberg terminal. This is a plain vanilla CZK interest rate swap, fixing the Prague IBOR. My task is to calculate zero rates from ...
0
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2answers
293 views

What Is the correct discounting, risky or riskless?

Suppose I can sell a European put in two ways: 1) in a mark to market collateralized market with collateral rate equal to the riskless rate $r$; 2) in a noncollaterized market where I get the payment ...
0
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1answer
72 views

Integrating Interest and Dividend Functions

How are interest rate and dividend functions integrated over time in practice? For example, what does it mean in practice to discount a current price by $e^{\int_{t_m}^{T}r_s ds }$ where $r_s$ is the ...
0
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1answer
176 views

example regarding zero coupon bonds

This example is from Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective by Carmona, René, Tehranchi, M R. I am wondering if the calculation is correct?, he says ...
0
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0answers
79 views

Mark-to-market cross-currency basis swap valuation

I'm looking to replicate the EUR vs USD cross-currency basis curve that Bloomberg outputs (EUR.OIS collateralized in USD). I understand that Bloomberg is currently using the mark-to-market ...
0
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0answers
41 views

What discount rate should I use in domestic/foreign context?

I am trying to price a quanto option by monte carlo simulation via quanto adjustment. SDE: $dS_t^f=S_t^f(r_f - \rho \sigma_s \sigma_{d/f})dt + S_t^f\sigma_s dW_t^d$, where $S_t^f$ is the underlying ...
0
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0answers
55 views

What is the use of undiscounted Futures/Option Prices

Reading the great book of Gatheral on Vol Surfaces (link) I can't help but notice that throughout he uses undiscounted option prices (though he obviously never assumed rates to be zero). See e.g. ...