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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Can you actually earn the carry return in FX? [closed]
I know that carry is an important factor to value currency. However, it is not obvious to me how you can actually earn the carry return, and if as a pure currency investor, should not you be ...
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Quantifying the impact of rates change on bond prices
How can I quantify the impact of a change in interest rates on bond prices?
I know that in a classical textbook setting the answer would be to compute the modified duration of the bond and, to account ...
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Can you use a forward rate curve to infer the SABR model parameters?
I am currently doing a thesis on a class of SDE parameter inference methods and using the SABR model as an example for inference. I want to extend the application to market data. My question is does ...
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Questions on options cost of carry, and relationship to futures cost of carry
I'm trying to grasp what exactly the effects of higher ongoing interest rates are on holding calls/puts. I am not asking what the effect of a change in interest rates is on call/put prices.
I'm ...
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Most relevant papers on IR / discount rate(s) modelling in the last 5 years
As the question states, what are some relevant recent papers I, as a non-expert, should read on IR modelling, products, and mechanics (that do not involve AI/ML)?
I think my knowledge on this topic ...
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Equality between ECB and IBMM rates
Regarding European Interbank Money Markets, at the beginning of each month, when the ECB performs LTRO operations, whereby it lends for a 3-month period, shouldn't the 3-m Euribor exactly match the ...
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Is it better to pay \$1 today or \$1 tomorrow? [closed]
I get from the time value of money that receiving \$1 today is worth more than receiving \$1 tomorrow. But what about paying money, as opposed to getting money. Do i prefer to pay \$1 tomorrow than ...
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Can volatility assume negative values under multi-factor HJM framework?
I could find any reference restricting the sign of the volatilities in the multi-factor HJM framework.
Can someone please confirm if $\sigma_i(t,T)$ can assume negative values for some $i,t$ and $T$?
$...
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How does Bloomberg calculate Interest Rate Caps/Floors with Black Scholes Merton Model and Volatility set as "Normal"?
While valuing Interest Rate Caps/Floors in Bloomberg, I saw that we have an option for selecting both Model and Volatility. So, my question is how exactly does Bloomberg value the cap/floor, when we ...
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Is there a way to use normal volatility in the Black–Scholes–Merton model to value interest rate caps? [duplicate]
I am trying to understand if there is a version of the Black–Scholes–Merton model that can use Normal volatilities instead of Lognormal volatilities while valuing interest rate caps and floors?
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What made SVB Bank to be uniquely negatively affected by higher interest rates? [closed]
For normal banks, higher interests means more profits. Why is SVB Bank the opposite?
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pricing in the case where payment currency and collateral currency are different?
I'm asking for the curve construction of the discount curve in the case where payment currency and collateral currency are different.
If I refer to BBG, in the case of a USD swap collateralized in EUR,...
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Replication Proofs and No-Arbitrage Proofs
I've just started studying quantitative finance and have had questions closed on this forum for being too basic; if that's the case for this one please let me know a more suitable place to ask.
Assume ...
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Understanding how markets predict BoC's policy interest rate decisions
I read in the newspaper things like,
Interest rate swaps, which are based on market expectations about future rate decisions, are pricing in at least one Bank of Canada rate cut later this year, and ...
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One Period Risk Neutral Probability for Caplet
I am studying some financial modeling put together by the Society of Actuaries in the USA. In it, the following practice problem was given:
Find the Risk Neutral price of an at-the-money interest ...
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What is the PDE for this interest rate derivative?
We have the following model for the short rate $r_t$under $\mathbb{Q}$:
$$dr_t=(2\%-r_t)dt+\sqrt{r_t+\sigma_t}dW^1_t\\d\sigma_t=(5\%-\sigma_t)dt+\sqrt{\sigma_t}dW^2_t$$
What is the PDE of which the ...
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How can Commercial Paper Spreads be Negative?
Looking at the spread between 3 month commercial paper and the 3 month bill (using say, Fred), how/why (economically speaking) can this spread be negative? Are there some mechanics in the commercial ...
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Pricing and hedging caps and floors on illiquid emerging markets
I'm tasked with the problem of setting up a cap/floor trading on an emerging market which doesn't have any interest rate derivatives traded yet besides plain vanilla interest rate swaps. We intend to ...
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How do sell-side institutions manage interest rate derivatives books in practice?
I'm interested in real practices of hedging interest rate caps and floors. There are plenty of articles explaining pricing of interest rate derivatives, but not so many explaining hedging such ...
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Why is SONIO Index lower than UK Rates? [closed]
The current UK Rate is 3.5. However, SONIO index is at 3.4269.
What is the reason for SONIO Index being lower than UK Rates?
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Is this the correct discretisation of the Hull-White SDE for building a python model?
I've tried to build a basic one-factor Hull-White model using python, which I've done by trying to discretise the characteristic SDE.
According to my notes, the Hull-White SDE is
$$
dr_t = \alpha (\mu(...
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OIS Swap P&L Calculation
Suppose I received RBNZ Nov OIS swap (start date 23 Nov'22 - maturity date 23 Feb'23) that I dealt on 10 Nov'22, at 4.1%. I unwind the trade by paying 4.25% (start date 13 Dec'22 - maturity date 23 ...
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Intuitive way to think about Bond Futures in a long only cash portfolio
I think this is the intuitive way to think about specialness in bond futures, at least to my mind; therefore, I am wondering if my logic is correct:
Cash Bonds have a forward price that is totally ...
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Cost of Carry of a Steepener using Treasury futures
I want to get a sense of the cost of carry (pure carry in this sense - no rolldown) embedded in a dv01 2s5s steepener in treasury futures. The horizon is 3 months, or 0.25 years.
The implied-repo rate ...
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Calculate Carry from Z-spread to Forward Spot Curve
I am considering a 5-year bond. I can buy this 5-year bond today, or I can buy it 3 months from now.
My question pertains to carry on the forward position. If I buy the bond forward and use the ...
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How does one calibrate a Vasicek model to actual cap prices?
I am trying to calibrate a Vasicek model given by
$$
dr(t) = k[\theta - r(t)] dt + \sigma dW(t), \quad r(0) = r_0
$$
where $k, \theta, \sigma, r_0 > 0$. I am using the book by Brigo and ...
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Is it possible to have negative beta terms in the Nelson-Siegel model?
The Nelson-Siegel model as described in this paper has the following form:
$$ y_t(\tau) = \beta_0 + \frac{(\beta_1+\beta_2)(1- e^{(-m/\tau)})}{\frac{m}{\tau}} - \beta_2e^{(-m/\tau)}
$$
Can the $\...
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Typo in Wilmott's Forward rate formula?
I am going through the 2nd edition of Paul Wilmott on Quantitative Finance, and came across the following,
Shouldn't the last equality be
$$
F(t;T) = y(t;T) + \color{red}{(T-t)}\frac{\partial y}{\...
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How does one put on a 2s10s trade using 2 and 10 year treasury futures contracts when the CTDs are not 2 and 10 year bonds?
The CME describes how to put on a 2s10s trade in this screenshot:
https://i.stack.imgur.com/2yPzW.jpg
Looking at current 2 and 10 year futures the CTD is roughly a 2 year and 7 year respectively.
Am I ...
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How to choose limit prices on IR futures when targeting a specific 2s10s spread?
I understand the concept of DV01s and when doing an interest rate future trade I need to use about a 2:1 ratio when trying to trade the 2s10s. This is explained here:
https://www.cmegroup.com/...
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Confusion about Initial Pricing IRS with Dual Curves
This is my first time delving into dual curves, or multiple yield curves. A question struck me about using OIS discounting when choosing the swap rate of a new IRS.
Without multiple yield curves I ...
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Speeding up Cutting Edge Quantitative Models on GPUs? [closed]
I have a very strong interest in the use of GPUs in quantitative finance, and am in search of algorithms/simulations/models that can have their runtime heavily reduced by GPU computation.
What models, ...
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Calibrating Hull-White model using historical data
I'm in search of a way to calibrate a very simple Hull-White model with a constant volatility and a constant mean-reversion speed, purely based on historical zero rates.
$$dr(t) = (\theta(t) - \alpha ...
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Use of interest rate swaps in liability-driven investing
You probably have home across recent events in the UK bond markets. The Financial Times article "The reason the BoE is buying long gilts: an LDI blow-up" from Sep. 28, 2022 goes through why ...
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Balance Sheet Value of a Repo
I am relatively new to repos and I am trying to find out whether there is a standard practice for calculating balance sheet value of a repo. Are there any regulations that prescribe how banks shall ...
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Is there a dollar index against emerging market currencies
Is there a dollar index against emerging market currencies?
The conventional dollar index (ticker DXY) is just an index against a few developed market currencies (the DXY is a weighted geometric mean ...
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Expectations on real interest rates in China
How do market practitioners approach expectations of real interest rates in China?
For the US we would look at inflation-linked bonds and surveys, but what about China?
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How does Bloomberg bootstrap CASH Instruments?
Given the following datas :
If we do the bootstrap methodology for CASH Instrument we gotta :
Calculate the DF associated to the Market Quoted Rate (2.91157). For the 3M Fixing we have :
T = 0.26115.
...
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Convexity adjustment doubt
So this the question and the answer to the first one states that only the 5 year swap rate will be adjusted for convexity and the answer to the second one states that neither of the rates will be ...
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how to calculate the implied interest rates using STIRs futures?
I saw a post of trader sharing his expectations of implied interest rates on different meetings dates of different Central banks using STIRs ScreenShot and am trying to figure out how he did it ?
my ...
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How should we interpret r_c in continuously compounded interest? [closed]
I'm just curious there is any useful "meaning" or interpretation we can assign directly to $r_c$. Of course one can directly calculate the non-continuously compounded interest from $r_c$, ...
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Why is carry divided by DV01 to scale it?
If I understand correctly, 6M carry in a fixed-floating interest rate swap should be the difference between the fixed and floating leg.
When I read this on Page 2:
https://corporate.nordea.com/api/...
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From Implied volatility to shifted Black volatility
I don't know who to go from normal to shifted black volatility before calibrating SABR with negative interest rates.
I see: "As we know that implied volatilities have a one-to-one relationship
...
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Interest rate swap Profit and loss attribution
I am wondering how the IRS daily PnL will normally be attributed from trader's/market risk perspective.
Will it be broken down into three parts daily carry (Daily interest accrual), daily roll-down (...
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Vasicek Model: smile dynamics
I have come across the statement that the Vasicek model cannot be used to price skew / smile sensitive products: i.e. it cannot be calibrated to replicate a skew or smile. Why is that?
My guess is ...
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Estimating the relationship between short-term intretes rates and 10Y bond yields
On the 16th of March 2020, the Polish Central Bank announced its first-ever round of Quantitative Easing. I am conducting an event study on how this announcement impacted the term structure.
The main ...
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Term premium with daily vs monthly time series
I have estimated the term premium for the Polish Government Bonds (POLGBs) using the methods described by Adrian et al. (2013) (often referred to as ACM). The underlying yields are interpolated from ...
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Approximate dollar MTM of interest rate swaps
I'm definitely a fixed income tourist but I'm wondering if there's an easy way to back of the envelope approximate dollar PnL of an interest rate swap
For example, if I enter a $1m fixed 5y USD swap ...
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When using exponents the BA II Plus is returning incorrect answers, what am I doing wrong?
I am using the BA II Plus Texas Instruments calculator.
When I want to calculate an EAR for example, my calculation would be as follows:
(1 + r/m )^m -1 = EAR
So in my calculator, using 5 decimal ...
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