# 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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### Estimating Parameters - Vasicek

The Vasicek model for the short rate $r_t$ is given by the SDE $$dr_t = \alpha(\beta - r_t)dt + \sigma dW_t,$$ where $W_t$ is a Brownian motion under the physical measure. I'd like to compute bond ...
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### Zero Coupon Bond prices in One Factor Hull White model

I implemented the one factor Hull White model for educational purposes and I calibrated the model from a given (made up!) yield curve: The Zero Coupon Bond Prices from this yield curve are: Taking ...
193 views

### No arbitrage conditions for normal implied volatility

usually the term implied volatility refers to Black-Scholes implied volatility (also Log-Normal volatility): it is defined as a quantity which when plugged in the Black-Scholes formula returns the ...
627 views

### compute time from FX forward, how use DEPO rates?

assume I have following delta-term vol data from broker: ...
163 views

### Feller Condition (Cox-Ingersoll-Ross) source

For the Cox-Ingersoll-Ross model $$\text{d}r_t = a(b-r_t)\text{d}t+\sigma\sqrt{r_t}\text{d}W_t$$ the condition (referred to as "Feller condition") $$2ab\geq\sigma^2$$ ensures that the solution is ...
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### Implied Funding/Borrow Costs in Short-Dated ETF Option Prices

I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
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### Pricing interest rate options in emerging markets

I've been thinking how to price the early payment of mortgages in banks from emerging markets, where swaptions/caps/floors aren't available, and how to hedge this kind of options. At first I thought ...
129 views

### Optimal mortgage rate strategy

When buying a mortgage, you can choose to "lock in" a rate at any point within 60 days of your closing date. Once locked in, you can't revert. This makes it a secretary problem - in the traditional ...
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### What type of interpolation should be used in key rate perturbation models?

When perturbing a key rate in order to assess sensitivity of portfolio value, what sort of interpolation is standard? A book I am looking at says linear, but this seems pretty unrealistic to me--and ...
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### What are the trade offs when choosing a long term bond future to trade?

It seems that when trading long term bonds *** and choosing between the two offerings on CME one is presented with a Scylla and Charybdis decision. 1. VOLATILITY CONSISTENCY: Ultra U.S. Treasury Bond ...
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### Fixing mean reversion parameter in the 1F HW model

I am trying to calibrate the 1 factor Hull White model to ATM swaptions. The strategy which I use is to minimise the sum of squared difference between model and market prices for the swaptions on the ...
129 views

### Inflation/Rates Correlation

I've been looking into a short piece of maths a colleague has written on pricing inflation with payment delays, and was hoping someone could confirm whether my understanding is correct, or if my ...
190 views

### Bachelier Pricing Formula for Interest Rate Binary Options

Similarly to the Black and Scholes formula, I am looking to replicate Bachelier's caplet formula with two digital options: (1) asset-or-nothing (forward rate in this case) and (2) cash-or-nothing. For ...
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### Fed Funds Rate: longer maturities

FFR published by Fed Bank of NY is the average rate US banks charge each other for the overnight loans of their reserves required by the Fed regulations. Since Fed acts similar to a clearing house ...
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### Bond (yield curve) dynamics in the Forward-LIBOR-market-model

The standard Libor-Forward-Market-Models provides a way of modelling the evolution of forward rates in time. However the model does not seem to be well suited for the modelling of zero-bonds. But ...
638 views

### Reasoning for Bloomberg's short rate volatilty calculation

Bloomberg, in its documentation, explains that it calculates the short rate volatility for its Hull White implementation by multiplying the e.g. 10y IRS rate (divided by 100) by the 10y cap vol. Why? ...
156 views

### A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints

[I already posted this question on the math forum of stackexchange and I was advised that I should post this question here] In Evans and Jovanovic (1989) you will find a model for entrepreneurs with ...
965 views

### Yield Curve Volatility

Let you have several issuers, and let each issuer have its yield curve built up with liquid plain vanilla fixed rate bonds. Each yield curve has its slope and its curvature, and they obviously change ...
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### Questions about Markit rates curve bootstrapping

I am reading the following two Markit documents concerning the bootstrapping of respectively the USD rates curve and the EUR, GBP, JPY, CHF, CAD, HKD, SGD, AUD and NZD rates curves. (Both versions are ...
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### Ito's lemma for special case

Assume a HJM framework with the same Brownian motion driving the dynamics for every tenor. $$df(t,T) = \alpha(t, T)dt + \sigma(t,T) dw_t \,,$$ with $\alpha(t, T) = \sigma(t,T)\int_t^T \sigma(t,s)ds$....
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### How does this transformation for Euler Scheme in mean reverting SDEs alleviate instability?

I saw this text in the book - Interest Rate Modelling by Andersen volume 1 on Page 112: I am unable to understand: How does instability arise when we use the Euler scheme on X(t)? What change does ...
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### Discrete term structure models - generalized procedure to ensure positive probabilities across multiple measures

Question: Is there a generalized procedure for building a discrete (e.g. binomial) term structure model with risk-neutral branching probabilities that ensure positive probabilities under alternative ...
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### Why can the t-bill rate forecast stock returns?

The tbill rate is used as a predictor of the equity premium in a number of papers. Whilst there is not a general consensus about whether it is a significant predictor, it is still widely used. I ...
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### A Soft Problem: Application of Stochastic Differential Equations in Hilbert Space Beyond HJM Interest Rate Model

I am reading books on stochastic differential equations (SDE) in Hilbert spaces. It seems that every book just discusses HJM interest rate model as an application when discussing financial ...
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### Basic Question on rate hikes priced in through Eurodollar futures (EDF)

(Say) The Mar19 Future price is 94.52(5.48%) and the Dec 19 Future price 94.27(5.74%), does this imply that markets expect a ~25bps hike specifically between the time period when the two contracts end ...
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### Strategy in steepening curve environment, stable spreads - HotS interview problem

The following problem was found in "Heard on the Street": You construct a yield curve for (coupon-bearing) treasuries. A particular five-year corporate zero-coupon bond has a default risk ...
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### Interest model calibration and binomial trees

Are there any good books for beginners on calibrating interest rate models and creating binomial trees based on these interest rate models and using them in pricing
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### How do markets price an interest rate rise?

It is common to see phrases like Markets priced in a 68 per cent chance of a rise in UK interest rates at the next meeting, up from 48 per cent before the June decision was announced This example ...
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### Hull White and HJM model not Markov

In HJM model we have instaneous forward rate $f(t,T):$ $$d f(t,T) = v(t,T)v_T(t,T)d t - v_T(t,T)d W_t,$$ is ...
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### How do traders determine when points in a yield curve are at 'fair value'?

While on my last day on an internship last summer, I heard on the morning call a UK rates trader say something along the lines of: "Most of the curve is at fair value at the moment, so nothing ...
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### 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 ...
316 views

### Ho-Lee Model Calibration: theta becomes smaller

This question is regarding the Ho-Lee model: $$dr_t = \theta_tdt + \sigma dW_t$$ In discrete time, we can calibrate an interest rate binomial tree by finding $\theta$ in each period to match ...
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### Code for quasi-Gaussian model (Cheyette model)

I'm looking into the quasi-Gaussian model with linear local volatility as explained by Andersen and Piterbarg (Interest Rate Modeling, Volume 2). I'm trying to calibrate this model and implement it. I ...
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### Are forward rates starting at observation date spot rates?

In part 3.2 of Lu and Neftci (2003) "Convexity Adjustments and Forward Libor Model: Case of Constant Maturity Swaps", the authors propose a new way of pricing CMS swaps, with Monte Carlo simulations. ...
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### Interpolation of forward zeros-coupons bonds simulations for missing maturities (ESG data)

I have a set of economic scenarios simulated with Barrie and Hibbert ESG. The stochastic model for interest rates used is Libor Market Model Shifted. I am facing a problem with zeros-coupons prices. ...
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### Can I use these rates for ACT/360 discounting?

I have calculated forward rates like this: $r_{t_1,t_2} = \left(\frac{(1+r_2)^{d_2}}{(1+r_1)^{d_1}}\right)^{\frac{1}{d_2-d_1}} - 1$ I want to find the discount factors for these forward, with ACT/...
I'm trying to calculate the expected value, at time $0$, of a cashflow paid at time $T$, resetting at time $t$. The coupon is of the form: \$V_0=\mathbb{E}^{T_2}\left[\frac{A_t^y(T_1,T_2)}{B_t^x(T_1,...