# Questions tagged [discounting]

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### Interest rate calculation [closed]

The task: With what interest rate given 2000 Euros after 2 years and 3000 Euros after 4 years, the actual value will be equal 4000 Euros. This task sounds confusing for me, I tried to calculate, but ...
51 views

### Formula for the discounted payoff of a digital option

In "Heard on the Street" it states that the expected discounted payoff of a digital option is $$H\exp^{-r(T-t)}N(d_2)$$ where $H$ is the payoff of the option, the exponential is the discounting. ...
111 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 ...
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 ...
63 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. ...
216 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 ...
83 views

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

I understand the aspect that central clearing reduced counterparty risks. From the valuation side, am I right that cash flows for both trades will be discounted at the OIS rate? The party that holds ...
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?...
74 views

### 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 ...
32 views

### OTC equity option under foreign currency CSA

What adjustment do I need to make to the Black-Scholes equation when the CSA of an OTC equity option is in a different currency than the underlying in order to get the correct price? For instance, ...
107 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 ...
118 views

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

What instruments are the current industry recommendations for constructing money-market yield curves in some major currencies? The switch after the crisis to multi-curve methods is well documented on ...
54 views

### Can someone explain to me the intuition behind the discount factor for this simple payoff? [closed]

Let's say you enter into a contract today in which in time t, you receive the difference between the underlying stock price and 100. Denote the stock price as S. Why is today's value of such a ...
112 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: ...
384 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 ...
51 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 ...
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### 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-...
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### 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 ...
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 ...
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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### 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 ...
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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 $100 and I don't want to pay it all ... 1answer 119 views ### Discounted asset price is martingale in BS model I want to verify that the discounted stock price process$\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 $$\mathrm{d}\mathrm{e}^{-r(T-t)}... 0answers 85 views ### What is the use of undiscounted Futures/Option Prices Reading the great book of Gatheral on Vol Surfaces (link) I can't help but notice that throughout he uses undiscounted option prices (though he obviously never assumed rates to be zero). See e.g. ... 1answer 375 views ### ESTER replacement for EONIA/EURIBOR Does anybody know what impact the replacement of EONIA with ESTER ( Euro Short TErm Rate ) will have on discounting existing or new derivatives once EONIA will be restricted as of Jan 2020? I'm ... 2answers 122 views ### Calculation VaR on long term period I'm calculating VaR numbers from historical data for a single instrument (it's plain vanilla, not a derivative) and receive such variables: I could provide necessary data, and formulas but I guess ... 1answer 91 views ### Macaulay's Duration with Zero Rates The definition of Macaulay's Duration is the weighted average maturity of cash flows and is calculated as-$$D_{mac}=\frac{\sum_ttPV(C_t)}{V}$$where PV(C_t) is the present value of the cash flow ... 0answers 35 views ### Calibration of stock's intrinsic value under the gordon model Assume we have the constant growth Gordon model, for a stock paying dividend D,Earnings per Share EPS, annual growth rate g=ROE*(1-\frac{D}{EPS}) and discount rate r. Then: IV=\frac{D*(1+g)}... 1answer 2k views ### Cheapest-to-deliver (CTD) discount curve Can someone explain, in layman's terms, the mechanics (the algorithm steps) of the construction of the discount curve in the case when the CSA allows the posting party to choose a currency (from a ... 0answers 641 views ### Properties of Geometric Brownian Motion Integrated w.r.t. Time (i.e., distribution of a Yor Process) Let S_t be a process which follows a Geometric Brownian Motion: \frac{dS_\tau}{S_\tau} = \mu \,d\tau + \sigma \,dW_\tau By Ito's lemma, we have: S_T = S_t e^{(\mu-{\sigma^2 \over 2})(T-t) + \... 1answer 75 views ### In DCF, why is the discount rate interpreted as the minimum rate of return? Is there an intuitive explanation of why, in DCF modeling, the discount rate should be interpreted as the minimum rate of return? This doesn't make sense to me because I think of the NPV as "what all ... 3answers 164 views ### Does the traditional NPV formula of a cashflow double count risk? Consider a cash flow stream of a single payment (1 period away). Its net present value is typically presented as$$ \text{NPV} = {\text{EV}(\text{Cash Flow}) \over 1 + d} \tag{1}$$Here$d$is ... 1answer 617 views ### What discount rate for uncollateralized cross currency swaps? To expand on this question, what happens if the uncollateralized swap is of a cross currency variety? Ignoring any xVAs, it's unclear which currency would best determine the discount rate: a) we ... 2answers 212 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 ... 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 ... 1answer 271 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 ... 0answers 158 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 ... 1answer 8k views ### Discount Curve Vs Forward Curve This could be a trivial question, but would I like to clear the concepts. Our firm started sourcing the Murex Trades which has all the variety of Derivative products. I noticed that the Curve ... 2answers 4k 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. 1answer 211 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 ... 1answer 161 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 ... 1answer 684 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-... 1answer 162 views ### Up-front settlement of forward contract One has entered a forward contract to purchase oil at$F_{t,T} = S_{t}e^{(r_f + s - c)(T-t)}$. The contract is entered at time$t$and executed at time$T$. Where:$S_{t}$is the spot price at time$...
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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, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Net present value when cash flows accrue continuously and are stochastic

I am trying to find a closed form solution to a stochastic integral -- which is really just a generalized expression for the expected net present value, $E^*[V_t]$, of an annuity (or perpetuity if \$T \...