Questions tagged [interest-rates]
An interest rate is the rate at which interest is paid by a borrower (debtor) for the use of money that they borrow from a lender (creditor).
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What calculation professional use to know how much of interest rates the market is pricing [duplicate]
Whenever I read news articles on specific topic (interest rates ) especially before the fed meeting I see some titles stating that the market is betting/pricing for example 0.5% or 1% rate move ,and I ...
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Trying to check this 1Y1Y forward treasuries calculation
here is a screenshot of the FWCM screen on Bloomberg:
https://i.stack.imgur.com/2BT3y.jpg
I'm trying to check that I understand this by calculating the 1Y1Y which according to this matrix is 3.6877%.
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How to build an FX curve?
Apologies for the rather broad question! Essentially, I wanted to ask how to build an FX forward curve from scratch. I have some basic understanding of interest rates and discounting but I am lacking ...
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Deriving the variance of G2++ Model
I'm studying G2++ Model in Brigo(2007)'s book.
The model constructed as follows,
$$
r(t) = x(t) + y(t) + φ(t), \quad r(0) = r_0\\
$$
with the dynamics of $dx(t)$ and $dy(t)$ described by:
\begin{align}...
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MBS Index replication month-end flows
Several investors track indices to gain exposure to specific asset classes. And these indices may be re-balanced on a monthly basis, based on market-cap etc which generates month-end flows from ...
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Why did Ginnie Mae MBS Net issuance decrease significantly in 2020-2021?
Net Issuance of Agency MBS can be thought of as driven by Existing Home Sales, New Home Sales, Cash out Refis, Amortization and Non-Agency MBS runoff. Based on this definition of net issuance, is ...
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FX Swap PnL and NPV
Suppose I have an existing FX Swap, suppose the spot leg is already settled, so only forward leg is left.
Question: What will be the P&L for this instrument - only forward leg NPV or spot leg is ...
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MBS Dollar roll mechanics
Had a few questions on MBS Dollar rolls:
How are dollar rolls affected by Interest rate Volatility?
Does the OAS of underlying pools matter to dollar rolls, and if so, how do they affect it?
Does the ...
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Dynamics of FX rate
I've see a couple of places where a FX rate, denoted $X$, such as EURUSD (quoted as "the number of USD needed to buy 1 EUR") is modeled with a diffusion process / Geometric Brownian Motion ...
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Determine if stocks are hurt by rates or recession fear
Looking at a portfolio of growth stocks which traded at high multiples until end of last year.
Stocks have been underperforming (no surprise there) but I'm trying to find ways to determine, ...
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MM Proposition and the cost of debt
I was studying Miller-Modigliani theorem and one of the stated assumptions was that there will be no bankruptcy cost to the firms.
Does the assumption of "no bankruptcy cost" assume that in ...
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Interest rate risk of a bond as a function of the coupon
This SEC document claims that increasing the ocupon on a bond decreases the interest rate risk (bottom of page 3):
And the Finra SIE exam states the same also.
I cannot understand the logic behind ...
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falling flatforward curve in quantlib
I am trying to create a floating rate bond where I need to create a flatforward curve, but the curve seems falling over the time, or is there any way to keep the rate constant.
...
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Difference HJM Framework versus Short rate model
Recently I study some interest rate models.
When I moved on to forward rate models, I see this documents
https://en.wikipedia.org/wiki/Heath-Jarrow-Morton-_framework
It said "HJM-type models ...
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Trying to learn to bootstrap with the Treasury Curve and can't seem to get a result that makes sense
I'm trying to learn to bootstrap and am taking some bonds from the Treasury curve:
https://docs.google.com/spreadsheets/d/1vA7s4ZfFzGfTji_d9cLUid5rqyaugRrI0etCW_3Jb6w/edit?usp=sharing
For some reason ...
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Determine forward rates for EUR/USD
I can't wrap my head around how to determine the interest rates to calculate the forward rates of any currency. At this point, I don't even know if this data is actually available to do the ...
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Uncovered interest rate parity
I know that empirically the uncovered interest rate parity fails. But let's set that aside for a moment.
The uncovered interest rate parity says:
$$(1+r_{USD}) E_{EUR,USD} = (1+r_{EUR}) $$
where $r_{...
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Calculating Risk Free Interest Rates for VIX formula
This question pertains to a whitepaper published by the CBOE that explains how the VIX index is calculated.
Near the bottom of page 5 of the whitepaper, it explains that two risk-free interest rates ...
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Term SOFR rate formula
The following website gives the specifications of the CME Term SOFR reference rates: CME Term SOFR.
Point 1 in the link above specifies that the tenors that are currently supported are 1m, 3m, 6m, and ...
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Put call parity with real time tick data
I am working with some real time options tick data (mainly futures options and index options), and in many cases the quotes are single sided (as seen on bloomberg terminal). I will denote a quote as ...
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Market price of risk ($\lambda$) - Brigo and Mercurio
In page 52 of Interest Rate Models by Brigo and Mercurio the following is stated:
Precisely, let us assume that the instantaneous spot rate evolves under the real-world measure $Q_0$ according to $dr(...
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What is the Performance Total Return Swap (TRS)? How about Performance Fixed TRS and Performance Float TRS?
I just know these products recently: Performance Total Return Swap (TRS), Performance Fixed TRS and Performance Float TRS.
But cannot find a detailed explanation of the product, all I can find is an ...
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Zero Coupon Bond - Price and Yield when interest rate is a diffusion process and 0 "price of market risk"
Given that the price of market risk (or market price of interest rate risk) is $\lambda(r_t, t)=0$ and that we have the following dynamics of the interest rate (under the physical measure $P$.
$$dr_t =...
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Is the G2++ model apt to use when one needs estimates of longer term refinance rates for mortgages and can the model be created with Monte Carlo?
I am currently in the process of developing an interest rate model that would be used to price mortgage-backed securities and develop an OAS estimate. Referring to Brigo and Mercurio (2006) I'm ...
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Explain daily P&L by risk factor for a portfolio of bonds and FX forwards
I was once an intern for a small bank with a portfolio mainly composed of gov. bonds, FX Forwards and time deposits. We used to report the daily P&L along with a P&L atributtion to each of the ...
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Difference between OIS and SOFR?
Basic question: I am a bit curious what are the differences between Fed Fund Rate, OIS and SOFR? All three, as I understand are based on overnight collateralized transactions? (Please correct if I am ...
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Caplet stripping in the bwd-looking RFR world with/without maturity adjustment
Since the beginning of this year, LIBOR rates have ceased in some markets like GBP, CHF, and JPY and rates pricing has moved into the RFR space, using compounded overnight rates as the underlying for ...
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Global Country Index for Insurance
I am trying to create a global country index for insurance. So this would be insurance by country. Anybody who is an expert in econometrics can give me some guidance on how to do this? How would I go ...
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Analytical evaluation of the following caplet-type product under lognormal assumptions
Let $n \geq 2$, and consider a tenor discretization: $0 = T_{0} < T_{1} < ... < T_{n}$ and associated forward rates evaluated at time $t$, as $L_{i}(t):=L(T_{i},T_{i+1};t)$ for any $i = 0,...,...
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Number of Fed Rate hikes prices in
Could someone please explain to me how the calculation of the market expected FED rate hikes is done?
Thank you.
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SABR-LMM: best way to perform a MC simulation
I am working on a SABR-LMM model with the following system of SDEs under a numeraire $N$:
$$
\begin{align}
&\mathrm{d} F_i(t) = \sigma_i (t) (F_i(t) + s)^{\beta} \Big( \mu^f_i (t) \mathrm{d}t ...
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Differential vs. derivative in the Vasicek model [closed]
Can anyone help me in understanding how we get the line I have marked with a red arrow?
I guess I have trouble in understanding the difference between differentials and derivatives, i.e. what is the ...
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Italy Zero Coupon Yields
I am looking for historical data for Treasury bills and bond yields for Italy on a monthly or daily basis. Where can I get this data?
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Is there anyone trading Then-Current Treasury Forward?
The treasury forward traded for those on-the-run or off-the-run makes sense. You simply trying to hedge the treasury bond already issued by calculating the forward price of the bond.
I was wondering ...
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Finding the distribution of $I(T_{1},T_{n})$ under an appropriate measure if the forwards are lognormal? [duplicate]
My question follows beneath the "lengthy" setting I describe:
Given a tenor discretization $0 = T_{0}< ... < T_{n} =T$,
and under the assumption that under $\mathbb P$, for all $i = 1,....
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Inferring a term structure when using a short-rate model
I'm relatively new to working with interest rate models and I am having some conceptual difficultly considering how a short-rate model can be utilized when calculating OAS of a mortgage-based bond, ...
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If any zero coupon bond $P(T)$ can be chosen as a numéraire, then why can the rolling bond for any time discretization be chosen as numéraire
Let us consider some finite time horizon $[0,T]$, and we assume that $P(t)$, the zero coupon bond maturing in $t$ for any $t\in [0,T]$ can be chosen as a numéraire, i.e. such that the numéraire-...
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IR risk sensitivity to curve instruments
I need to understand if the 2 approaches are equivalent:
assume I am constructing a yield curve with N instruments. I would like to compute IR delta for a product using this curve. One approach is to ...
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equivalentRate not matching for compounding cashflows
I am calculating equivalentrate between two days in quantlib python using following functions but the output is not matching with the manual calculation.
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Replacement for LIBOR Market Model (LMM)?
With the transition from LIBOR to SOFR, will the LIBOR Market Model be replaced by a new model? Perhaps this has already happened. If yes, what is this new model? If not, will the LIBOR Market ...
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Why would valuation for a swap be the same on the backward and forward rate but not a caplet
Consider for time discretization $0 = T_{0} < T_{1} <... < S < T < T_{n}$, and the corresponding forward rates and backward rate:
$\text{Forward rate: }L(S,T;t)$
$\text{Backward Rate: }...
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Should Cross-Currency Basis Swaps exchanging risk free rates trade flat?
In the paper "Interest Rate Parity, Money Market Basis Swaps, and Cross-Currency Basis Swaps" by Bruce Tuckman and Pedro Porfirio (2003) the authors claim that cross-currency basis swap ...
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Assymetric Rate Distribution
The pandemic has disavowed any notion of nominal rate distributions to being truncated at 0%. However, if Central Banks at Debtor nations are conflicted in that they are incented to suppress interest ...
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In the Black-Scholes model with stochastic interest rates, what are the 3 assets used to compute measures?
Suppose I have a model with 2 primary assets, a stock $S$ and a short rate.
The stock will be driven by a Brownian motion $W_1$. The short rate will be random and will be driven by a Brownian motion $...
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Does IRR (and therefore YTM) assume that all cashflows are reinvested at the IRR (or YTM)? If so, how does IRR the formula show this?
There are many articles I have read recently that say the reinvestment of interim cashflow idea in the IRR is a fallacy though I am not sure who to believe since so many resources, for example ...
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Modelling Bank deposit with replicating portfolio
I am trying to understand how deposits in bank are modelled, and one such modelling approach is replicating portfolio approach as provided in http://www.diva-portal.org/smash/get/diva2:1208749/...
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Replicating a bond
In Shreve's Stochastic Calculus for Finance Volume II, section 6.5, page 273, Shreve talks about pricing a zero-coupon bond.
A zero-coupon bond is a contract promising to pay a certain "face&...
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How to find the risk neutral valuation of $P(T_{1})$ und the measure $\mathbb Q^{P(T_{2})}$
How do I find the risk neutral valuation of $P(T_{1})$ und the measure $\mathbb Q^{P(T_{2})}$, where $P(T_{1})$ and $P(T_{2})$ refer to the $T_{1}$ and $T_{2}$ zero coupon bond with $0 < T_{1} < ...
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What adjustments need to be made before a Monte-Carlo simulation can be applied for the exotic option $(L_{\text{domestic}}-L_{\text{foreign}})^{+}$
I just want to reassure myself that I understand why Monte-Carlo is the appropriate tool in computing the fair value prices for different options. Let's say we have a Tenor discretization $T_{0}=0<...
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How does the market derive market implied rates hike via swaps?
It is the story of interest at the moment. Rate hike expectations from central banks around the globe. Various sale side research parties publish often market implied rates hike. The magnitude and the ...
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