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).
1,032
questions
2
votes
1
answer
253
views
Multi-factor vs Single-factor interest rate model for XVA / CCR
When calculating XVA or Counterparty Credit Risk (CCR), you can choose to simulate your interest rate with a Multi-factor interest rate model or a Single-factor interest rate model.
What are the pros ...
- 483
2
votes
1
answer
867
views
Proof of the Hull & White Model calibration
I have a question about the demonstration of the formula which states that:
If we have an Hull & White Model for the short rate diffusion such that
Then the model is fully calibrated if and only ...
- 267
2
votes
1
answer
173
views
Why Arent There Long Rate Models?
You have short rate models, https://en.wikipedia.org/wiki/Short-rate_model, but there doesnt seem to be any long rate models.
I find this weird as in options modelling you model the whole smile, not ...
- 2,492
2
votes
1
answer
140
views
Recreating / Extending Bond Time Series
I am trying to analyse historical yield curve dynamics within an across countries and step one is extending / recreating historical yields and/or prices.
The challenge is this: lets say a 10 year ...
- 176
2
votes
1
answer
805
views
How do swap dealers make money from trading cancellable swap?
A fixed-rate payer (e.g. a swap dealer) of a cancellable swap pays more interest than he receives because he has the right to terminate the swap after a certain time if rates fall. What are the ...
- 21
2
votes
1
answer
771
views
From continuous compounding to simple compounding - convexity adjustment
I have derived the convexity adjustment expression for futures rates using the Ho-Lee model, to arrive at the following:
$$
ForwardRate = FuturesRate - \frac{1}{2}\sigma^2T_1T_2
$$
where $T_1$ refers ...
- 223
2
votes
1
answer
2k
views
Hedging with interest rate futures, different duration
This is from Hull, problem 6.16.
Suppose that it is February 20 and a treasurer realizes that on July 17 the company will have to issue \$5 million of commercial paper with a maturity of 180 days. If ...
- 163
2
votes
1
answer
223
views
Determining discount factors for non-standard maturities
Let's say we'd like to find a par rate for a 1 month forward starting 20-year interest rate swap. In this case, we'd need to discount cash flows for the payment periods shifted +1 month from standard ...
- 989
2
votes
1
answer
375
views
Introducing 1bp shocks to yield curve (and interpolation consequences)
Let us assume we have a LIBOR 3M curve and that I would like to introduce a small shock up/down of 1bp at a certain point along the curve. I am trying to find out what the best and most efficient way ...
- 473
2
votes
2
answers
503
views
Pricing a Vanilla swap between coupons; What rates to use?
Vanilla Swap question.
Entered into a 5Y fixed for floating HUF swap. Fixed is annual coupons, Float is semi-annual coupons.
1 month later I want to price it. I set up my future values for Fixed ...
- 21
2
votes
1
answer
293
views
how to compute the risk free rate for a given maturity of an option contract?
i'm working on options with different maturities. I need to correspond a risk free rate for each maturity. What rate should i consider as risk free rate?
thank you.
- 23
2
votes
2
answers
588
views
Bond Prices in terms of short and forward rates
Of course, a pure discount bond price $P(t,T)$ may be stated in terms of its yield $R(t,T)$ as
$$
P(t,T) = e^{-R(t,T)(T-t)}.
$$
Let's assume both the (instantaneous) short rate $r(t)$ and (...
- 2,828
2
votes
1
answer
202
views
Fed FOMC Target Rate annnouncement machine readable data point
Does anyone know if there is a near-realtime machine-readable feed that reflects the FOMC target rate announcement? The announcement came in today at 2 pm, but I can't find a way to download the ...
- 151
2
votes
1
answer
379
views
Function A(t,T) in one-factor Hull-White model
I am struggling with Hull-White model now and have the following question: in the lecture notes under the link below I see how A(t,T) and B(t,T) are being derived. This requires the solution of ...
- 55
2
votes
2
answers
6k
views
Historical calibration of Hull-White model
I have a question concerning 1-factor Hull-White model. For my master project I need to calibrate it to compute Counterparty credit risk metrics. I know that the model might be calibrated either for ...
- 55
2
votes
1
answer
3k
views
Why is my YTM incorrect? How does accrued interest play into Yield to Maturity?
I'm writing some software that includes a feature to calculate Yield to Maturity for a Bond. I'm using an HP 10bii Financial Calculator to double check the answers produced by my software. I'm running ...
- 121
2
votes
1
answer
1k
views
Calibration of Heston version of CIR
I'd like to calibrate a variant of Heston model for interest rates which is describe by this couple of SDE
\begin{aligned}dr_t&=a(b-r_t)+\sqrt{r_t}\sigma_t dW_t^1 \\ d\sigma_t&=k(\theta-\...
- 151
2
votes
1
answer
374
views
Negative Eonia rates
I'm curious how the current negative Eonia (Euro OverNight Index Average) rates would impact derivatives pricing. Does it mean that if I post cash collateral to you, I also need to pay you interest?
...
- 2,265
2
votes
1
answer
2k
views
Risk-Free Rate determinant in CAPM
I have trouble understanding what type of maturity to use when calculating CAPM. My professor uses the 3-Month risk-free rate to ...
2
votes
1
answer
131
views
if market is always assumed right, what happened when LIBOR was manupulated?
Recently Monetary Authority of Singapore (MAS) raps banks in rate-rigging. This is nothing new, LIBOR was also manupulated before, by some "major" banks.
however, before the censorship, did any "...
- 2,231
2
votes
1
answer
120
views
Annual Percentage Rate and Yield
I found references relative to US where the Nominal Annual Percentage Rate or simply APR is defined as the simple interest rate (i.e. proportional to time and without compounding).
Instead the ...
- 253
2
votes
1
answer
147
views
How does the interest rate affect the implied volatility of options, especially ITM?
What would be a good reference to understand how the interest rate (r) or dividend yield (q), and I guess the differential between the two, affect the implied volatility of the options?
If I look at a ...
- 165
2
votes
0
answers
88
views
Measure of the behavior of Swaption surface
I'm looking to find a different measure than average shift move to explain the behavior of the IR VOL products say Swaption. I know it's a very open question not only touching upon IR VOL scope.
Let ...
- 21
2
votes
0
answers
113
views
Interest rate derivatives market data - download [closed]
EDIT; I looking for sources where from I could get interest rate derivatives market data? (caps,floors,swaptions, etc, is there data available for exotics ones or are they purely OTC?)
I would grade ...
- 21
2
votes
0
answers
144
views
How do forward-looking forward rates in the Mercurio's and Lyashenko's normal or extended FMM model represent EURIBOR rates
(By XIBOR I intend any EURIBOR or LIBOR rate. By RFR I intend SOFR for the USD and ESTR (€STR) for EUR.)
I am mainly focused on the EUR rates market (but also a bit on the USD market) and looking for ...
- 1,223
2
votes
0
answers
69
views
ATM cap prices in Vasicek model (Filipovic)
I am trying to replicate the ATM cap prices in table 7.1 (see bottom of this post) from Filipovic's book "Term Structure Models - A Graduate Course" which assume the Vasicek model and uses ...
- 548
2
votes
0
answers
90
views
Black-Karasinski & Market Price of Risk [closed]
I have implemented the Black-Karasinski model using trinomial trees and calibrated following Brigo (2007) page 29. However, the results do not fit the interest rate curve practiced in the market. As I ...
- 21
2
votes
0
answers
150
views
Bond-pricing under the Vasicek short rate model
I'm currently studying the Vasicek model of the short interest rate
$$dr_t=a(\mu-r_t)dt+\sigma dW_t$$
I know how to solve this stochastic differential equation (SDE) and how to find expectation and ...
- 21
2
votes
1
answer
358
views
FRTB Delta CSR vs Delta GIRR
In Basel III, FRTB SA includes different market risk capital requirements for interest rate (GIRR §21.19) and credit spread risk (CSR §21.20) exposures. These are different risks, as credit spreads ...
- 525
2
votes
0
answers
446
views
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 ...
- 195
2
votes
0
answers
147
views
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 ...
- 65
2
votes
0
answers
83
views
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 ...
2
votes
0
answers
39
views
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, ...
- 527
2
votes
0
answers
26
views
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,....
- 83
2
votes
0
answers
839
views
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 ...
- 439
2
votes
0
answers
181
views
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 $...
- 51
2
votes
0
answers
236
views
Bermudan Swaption Pricing via Least-Square Monte Carlo
I have some confusion regarding pricing a Bermudan Swaption using LSMC.
Let's say the underlying swap has payment dates $T_0 < T_1 < \ldots < T_n$ and for simplicity, assuming the exercise ...
2
votes
0
answers
379
views
Derivation of the distribution for a CIR process
Where is it possible to find a complete derivation of the distribution of a CIR process?
There is a number of papers that claim that it is a noncentrical chi-squared distribution.
However, I cannot ...
- 21
2
votes
0
answers
147
views
Pricing kernel representation
I am reading this paper https://mpra.ub.uni-muenchen.de/4969/1/MPRA_paper_4969.pdf pp.6-7 on discrete-time bond pricing. The model adopted is a a common affine model,
the short rate follows
\begin{...
- 21
2
votes
0
answers
368
views
Swaption extrapolation
I have some ATM swaption volatilities with the following characteristics:
(-IBOR) payment frequency: 1M
Underlying swap maturities (tail): 1Y, 2Y, 5Y, 10Y, 15Y and 20Y
Swaption expiries: 1M, 3M, 6M, ...
- 21
2
votes
0
answers
112
views
What makes modeling interest rate derivatives very difficult compared to equity derivatives?
I understand while equity derivatives require the modelling of stock price at expiry, interest rate derivatives typically require modeling both the expiry and tenor, thus increasing the dimensionality ...
- 21
2
votes
0
answers
1k
views
How to find the risk-free rate and dividend rate for S&P 500 index options?
I'm currently working on a project using S&P 500 index options(European) data. I haven't done any empirical experiments before, so I'm confused how to find the corresponding risk-free rate and the ...
- 101
2
votes
1
answer
875
views
Under Put-Call Parity, why do we add the cost of carry to Call prices but subtract them from the Stock price and Put prices?
In Natenberg (1994) Chapter 11 he outlines the Put-Call parity relationships.
...
user46424
2
votes
0
answers
294
views
How to optimise Fixed Income portfolio (Yieldbook) based on YTM, duration, rating and exchange rate
I have a fixed income portfolio built up in the Yieldbook and BBG Port.
However due to some bad performance of my portfolio compared to the benchmark I would like to build up an optimisation which ...
- 326
2
votes
2
answers
272
views
Local v/s global calibration for a Bermudan Option (calibrate co-terminals vs entire matrix)
I am quite new to rates modeling and I have a question on the pros and cons of calibrating to larger set of vanilla instruments v/s calibrating to an exotic's 'natural' hedges. For example, I could ...
- 2,045
2
votes
0
answers
134
views
Building up an Economic Scenario Generator [closed]
I am trying to build an Economic Scenario Generator in VBA or Python. Can anyone please help me with some good resources which I can follow or some basic procedures which explains how to go about in ...
- 21
2
votes
0
answers
21
views
Estimating Product Rate Sensitivity to Market Rate Changes: First Difference With Interactive Variable
I am currently trying to understand and estimate the sensitivity of deposit rate sensitivity to market rate changes. My current model:
$\Delta$$R_t$ $=$ $\alpha$ $+$ $\beta_1$$*$$\Delta$$FFR_{t-1}$$+$...
- 21
2
votes
0
answers
32
views
Formulating Deposit Rate Sensitivity to Market Rate Changes
I have historical deposit rate data for a specific bank. I want to determine the sensitivity of deposit rates to market rate changes (I'll be using Fed Funds rate). My question is, what would be an ...
- 21
2
votes
0
answers
112
views
Understanding APR via programming [closed]
I am trying to better understand different types of interest rates. However, I am having difficulties complete, consistent and pedagogically-efficient explanations online. Thus, I have decided to ...
2
votes
0
answers
432
views
Difference in utility of cap/floor and FRA
What is the difference in utility for cap/floor and FRA? To me their function looks very similar. Are they used for different objectives. One thing I know in difference is that the pay off for cap is ...
- 123