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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For which interest rates r is the model arbitrage-free?
Given $\Omega=\{\omega_1,...,\omega_4\}$ and a probability measure
$\mathbb{P}$ on $(\Omega, \mathcal{P}(\Omega))$ where
$\mathbb{P}(\{\omega_i\})>0$ for all $i$. Let, furthermore, $r\geq 0$,
$S_0=...
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Cheyette Model vs Markov Functional Model
Just like to understand more about the model difference between 1d-Cheyette Model vs 1d-Markov Functional Model.
Is there a model difference betweeen these 2?
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Futures and Forward prices under the Heston model and their spread
This might seem like a very trivial question but I am really not so sure about it so I thought I post it here.
Assuming a Heston model of the form
\begin{eqnarray}
dS &=& (r-q)Sdt + \sqrt{v}...
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How can I use Monte Carlo to price a Zero-coupon bond in the Cox-Ingersoll-Ross model?
Let me prefix this by saying that, yes, Cox-Ingersoll-Ross (C.I.R.) is deprecated when used to model interest rates. Yet integrals of the form
$$P(0,T) = E\left(\exp\left(-\int_0^Tr_s ds\right)\right) ...
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Intuitive way to think about Bond Futures in a long only cash portfolio
I think this is the intuitive way to think about specialness in bond futures, at least to my mind; therefore, I am wondering if my logic is correct:
Cash Bonds have a forward price that is totally ...
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Is it possible to have negative beta terms in the Nelson-Siegel model?
The Nelson-Siegel model as described in this paper has the following form:
$$ y_t(\tau) = \beta_0 + \frac{(\beta_1+\beta_2)(1- e^{(-m/\tau)})}{\frac{m}{\tau}} - \beta_2e^{(-m/\tau)}
$$
Can the $\...
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Calibrating Hull-White model using historical data
I'm in search of a way to calibrate a very simple Hull-White model with a constant volatility and a constant mean-reversion speed, purely based on historical zero rates.
$$dr(t) = (\theta(t) - \alpha ...
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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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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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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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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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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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Is it true that interest rates options with different maturities are free of calendar arbitrage because of the different underlying rates dynamics?
The title says it all - is it true that European style interest rates options (lets say on LIBOR 3M for the sake of simplicity) with different maturities are free of calendar arbitrage because ...
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Replicating Bloomberg's zero rates bootstrapping
I'm interested in manually replicating the bootstrapping procedure that Bloomberg uses to built ICVS179 (RUB vs MosPrime 3M) curve up to a two years tenor as of October 12th 2021.
These are the market ...
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Calibrate 1-factor Gaussian HJM model on forward rates and ATM caps prices
I'm trying to solve the following problem as a part of the Interest Rate Models course
The algorithm that I'm following is
derive simple rates from the given forward rates via $L(0, T_i) = \frac{(1+\...
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Why is dividend discounted stock equal to cash discounted strike?
Doing some BS problem solving and came across this beauty:
$$S \cdot \text{exp}\Big(-D(T-t)\Big) \text{exp}\bigg(-\frac{d_{1}^{2}}{2}\bigg) = E \cdot \text{exp}\Big(-r(T-t)\Big) \text{exp}\bigg(-\frac{...
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Option Adjusted Spread - Monte Carlo
It's my understanding that in order to calculate the option adjusted spread on a mortgage backed-security, the following steps are required:
Run a Monte Carlo simulation of interest rates
Project ...
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Option pricing under Vasicek, CIR, H-L and BDT model
I have implemented and calibrated recombining trees on Excel for the Vasicek, the Cox-Ingersoll-Ross, the Ho-Lee and the Black-Derman-Toy model. I now would like to price some options with these ...
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Hedging Options assuming a non-constant Yield Curve
I have read most of Shreve's Stochastic Calculus for Finance II. In it, the author prices various option types assuming an interest rate that is constant with respect to time.
We can expand this model ...
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How to backtest with fixed-income instruments
I'm running a backtest with the 5-yr and the 30-yr treasury bills going back to 1990, both with a weighting of 25%. How do I use their daily yields to adjust the portfolio through time?
I've thought ...
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Interest rate risk calculation for Banking book
There is a detailed discussions on the Interest rate risk for Banking book. For Floating rate bond, this states like below -
such positions generate cash flows that are not predictable past the
next ...
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Interest rate model and premia with economical thinking
I heard the background about interest rate models from my coworker.
Especially it gives intuition to me that affine short rate model means it estimate long term interest rate by linearly add premia ...
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Cost of shorting currencies
I thought cost of hedging/going short on a currency with a forward was given by F/S-1 but it seems the author states 0.25% (see below). Am I missing anything (transaction costs, balance sheet costs, ...
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What is the name of this concept/formula?
I stumbled on this not so complicated concept and couldn't figure out what it's called.
I want to buy something that costs $M$ units of money, and have to pay it in $n$ months at a rate of $\frac M n$ ...
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843
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SOFR - calculation of the volume-weighted median and percentile
Federal Reserve Bank of New York web page provides some information on the computation of the SOFR rate.
Part 1
According to this webpage, the SOFR is calculated as the volume-weighted median:
"...
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CMS Convexity adjustment with negative interest rates
I need to price bonds with CMS-linked coupons. In order to determine the convexity adjustment to apply to the forward rates, I would use the formula that appears in Hull's Futures, Options and other ...
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How to link market risk and the transition to the new risk-free rates?
I'm a market risk analyst intern and I've the opportunity to do a project related to it. So I would like to move towards SOFR and €ster transitions, I have seen quite a lot of documentation on this ...
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Reconstructing bond proces with OIS rate
I am pricing derivatives under a $T$-forward measure and as such I need to discount the expected payoff with a bond price. I have available to me overnight-indexed swap (OIS) rates, how do I ...
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Use of Macaulay Duration to calculate the Funds Transfer Pricing Cost of an Amortizing Mortgage
I am asked to comment on the Funds Transfer Pricing methodology used by our Treasury to assign a Cost of Funds to a Loan. This is the current methodology:
Let us say there is a 2 year loan with an ...
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Vega hedging swaption with caplets - precisely, what will go wrong?
I am trying to form a kind of unified perspective of how (vega) hedging an exotic with vanillas, or hedging a 'basket option' with vanillas will go wrong. So in particular, I want to be able to ...
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Resources to calculate EIR
I'm looking for resources on calculations of effective interest rate across different kind of financial products like bond, term loans, etc.
Thanks!
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Calibrating Vasicek model for historical data
I need to to estimate the parameters of vasicek model to predict the zero curve.
My database has 4k daily observations of zero rate for 37 maturities. My question is do I have to estimate the model ...
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Calibration of G2++ two factor interest rate model using Kalman filtering
I'm trying to use the Kalman filter to calibrate a G2++ interest rate model in R. I'm reading "Implementing interest rate models: A practical guide" by Park F.C. (2004) where he provides details on ...
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Pricing of the compound coupon bond with PDE
I am now studying finance math using Steven E.Shereve's book.
Using Interest Rate models, We can the price for zero-coupon with maturity price $1$ under Hull-White interest rate model[page 274] and ...
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Arbitrage pricing models
I have been reading Wu's Interest rate modeling and in his chapter on the HJM model he says that
With arbitrage pricing models, the prices of the basic instruments are treated as model inputs ...
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What are good TEXTBOOK on stochastic volatility and interest rate theory?
I wanted to learn stochastic volatility modelling and interest rate modelling.
On this site, a answer recommended me the books "Stochastic Volatilty Modelling" by Lorenzo Bergmo and "Interest Rate ...
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Stochastic process with determinstic frequency of regime changes
Suppose that I have an OU process. For instance, assume that I want to model the interest rates. Suppose that regime change is known ex ante, and is deterministic in terms of frequency (For instance, ...
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Pricing call option on bond under CIR model by simulating noncentral chi square distribution
In the original paper of CIR model, there is a pricing formula about call option on bond
$$
\begin{array}{l}{C(r, t, T ; s, K)} \\ {=P(r, t, s) \chi^{2}\left(2 r^{*}[\phi+\psi+B(T, s)] ; \frac{4 \...
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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 ...
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Does Vasicek interest rate model had any derivation that follows from a list of assumptions?
I can't find that anywhere online and It doesn't seems to me that this model originated come from intuition or some human motivation but rather it is coming from computerized curve fitting as all the ...
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PCA predicted yield curve moves do not match (closely) realized yield curve moves
I have a need to set-up a methodology to decompose the x-day yield curve moves into its underlying (3) PCAs.
Specifically, for an example, to generate the 1-day moves in the EUR-swap yield curve; ...
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Duration and yield
I have some basic questions about mainly duration and yield.
1) Almost no-one defines what yield they are talking about when talking about duration and discount rate, I've seen some talk about ...
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Interview question on interest rate spread trade
Consider this interview question:
Tell me how you'd construct a risk neutral cross country trade on the 2 year – 10 year interest rate spread in Germany and the U.S.
What does "risk neutral" mean ...
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Duration of a FRN in continuous time interest rate model
This question was inspired by my attempt to understand the duration of a floating rate note, or FRN for short. Several answers, like this, say the duration of a FRN is just time to next coupon payment....
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291
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basic difference between interest rate models
I am reading up on interest rate models, but currently confused about difference in the two types of models:
no arb models like ho-lee, vasicek etc.
others like nelson siegel, pca models etc.
While ...
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LIBOR Market Model (LMM) - references
Could you advice me where I can find the best mathematical description of LIBOR Market Model theory (except the references from the Link). Is there any book/article/pdf file/web page/notes which you ...
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637
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Zero Coupon Bond Price under Hull White Model (One Factor)
While pricing Zero coupon bond using One Factor Hull White model:
$$dr(t) = \left(\theta(t) - a r \right)dt + \sigma dW(t)$$
How to determine the value of $\theta(t)$ using real world example:
$$θ(t)=...
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Extension of HJM to multiple factors
The HJM model calibrates the entire forward curve using the existing yield curve data and this results in the following expression for its instantaneous forward rate-
$$df(t,T)=\sigma(t,T)\int_0^T\...
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Relation between BDT volatility and Hull-White one factor Volatility
Is there any mathematical relationship between the volatility of spot rates calibrated from Lognormal model and the volatility of spot rates calibrated from HW one factor model?