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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6
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0answers
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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1answer
80 views

Concentration risk in Rates

What are some good ways to assess the concentration risk for a rates curve or by currency when volumes traded by instrument are not easily available? For ex, if for some currencies, the PV01 at ...
21
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1answer
509 views

What is the trickiest thing to get right in Rates Quant recently (2019)?

What are the biggest challenges for Rates Quants in 2019? Most quants have been through a lot over the past years-shifting their SABR models in JPY swaptions, fixing the FVA models for negative rates, ...
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1answer
56 views

Effective Annual Interest Rate (EAIR) in a 12-month loan [closed]

A \$980 loan is paid over 12 months in 12 equal payments of $90 each. What is the loan's EAIR? 980/12=81.666…. (monthly principal payment) 90-81.6666….=8.3333….. (monthly interest payment) ...
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0answers
31 views

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 ...
3
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2answers
63 views

Cash vs Deposit Rates

When constructing a yield curve for derivatives purposes, what is the difference between cash and deposits rates?
1
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1answer
371 views

How to calculate one-year forward one-year rate? [closed]

I'm just a little lost on how to calculate forward rates. I know this is an easy question, but, if we are given a one-year and two-year zero rate (let's say, for the sake of the argument, 2% and 3% ...
7
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1answer
494 views

CMS Pricing - Convexity Adjustment by Replication [closed]

I'm trying to learn CMS pricing, but didn't get the logic of this method. Previously cited articles about this method is pretty complex. I'd be glad if you can provide me with simpler articles or ...
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89 views

Curve Building + Swap Pricing [duplicate]

Assume Swap means a USD Swap with standard conventions (semi-annual fixed payments and quarterly floating payments, etc).
9
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3answers
385 views

Why is it useless to model stochastic volatility when pricing Vanilla style derivatives?

With respect to the answer by user AFK in Ideas about Stochastic volatility models. I am specifically interested in interest rate options (IR Caps/Floors and Swaptions).
2
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1answer
218 views

Reference books for interest rates modeling?

I'm interviewing for a rates modeling quant role in a sell side bank. The role is centered around pricing and risk management of rates trading carried out by the front office. I've been told to ...
1
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0answers
276 views

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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1answer
631 views

Shifted Log-Normal model

I am trying to understand how the shifted log-normal model works, in which we shift a log-normal model by a factor before the simulation so that interest rates don't turn negative during the ...
3
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1answer
98 views

Good References for Treasury Futures Spreads

I’m reading the excellent Treasury Bond Basis by Burghardt. I was wondering if there’s a similar quality book/paper about Yield curve spreads using treasury futures (i.e. NOL, NOB, FYT).
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1answer
115 views

Single vs Multi factor interest rate model

How do we explain the difference beween a single and multi factor interest rate model. Short term interest rate is one of the factor which is used in drift and vol calculation but what are other ...
2
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1answer
116 views

What is a central bank's shadow rate

I was reading a WSJ article about the European Central Bank shadow rate, which is -5.1% at the moment. The article says about the shadow rate that "Calculated with the rates on longer-dated credit ...
4
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0answers
53 views

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 ...
3
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4answers
459 views

Bond ETF vs Bond Future for longer term holding

How would a long term investor go about evaluating the prospect of investing in a bond ETF vs a long position in a future of equal duration? Let’s asume this investment is in a taxable account. Let’s ...
3
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0answers
191 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 ...
3
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2answers
5k views

How popular is the Linear Gauss Markov (LGM) model?

Some friends recommend to me Linear Gauss Markov model, saying it's interesting to have a look at it. Basically it's a framework different from HJM, with potential to extend, and the merit is that it'...
2
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1answer
481 views

Why Hull White 2 Factor model can't capture vol skew?

Is there a way to stay with the short rate model (like HW2F or G2++) but extend it to capture vol term structure (vol smile or skew). What happens if I calibrate HW2F to OTM swaptions? (I don't want ...
3
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1answer
799 views

Cap/Floor ATM Rate

This is a question on cap volatility market data. The quotes usually include volatilities for different strike (1%, 2%, ... 5%) and maturities (1Y,2Y,...20Y). One volatility for each combination of ...
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2answers
88 views

how to trade interest rates outside G10

G10 currencies markets have active FRA markets and apart from NOK, SEK and NZD one can also speculate on interest rates through exchange-traded futures. What's the best liquid way to speculate on ...
2
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1answer
2k views

What is the intuition behind the fact that Modified duration = Macaulay Duration / (1+r)?

I understand the derivation of both:take dP/dR and divide by P which will give you both 1) modified duration OR 2) macaulay duration / (1+r) (notice the weighted average time built into the function ...
2
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0answers
70 views

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 ...
3
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1answer
176 views

Modeling Interest-only Mortgages

Can we infer a range of future all-in costs for I/O ARMs with current index forward curves? Essentially, just taking a worksheet like this and adding some type of ramping capability after the fixed ...
1
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1answer
119 views

Derive a mathematical equation for Eurodollar future rate

If we suppose that r(t) follows a Vasicek model, which is: $$dr(t) = (\mu - \kappa r(t))dt + \sqrt\sigma dW(t)$$ How to derive an expression for Eurodollar future rate?
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1answer
87 views

Convexity adjustment--Assume sport and futures rates move together?

A cash flow argument I typically see for why a convexity adjustment is necessary is the following (taken loosely from Hull 9/e, p. 143): Say I am short an interest rate futures contract (e.g. ...
8
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1answer
1k views

Shape and geometry of the yield curve

Let the initial yield curve $T\mapsto y(0,T)$ be given for a term structure family of bonds $B(0,T)$ having different maturities. I am trying to figure out the geometric properties of the yield curve. ...
2
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1answer
307 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 ...
0
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1answer
87 views

Spreadlock derivatives

I would like to price a spreadlock forward swap and a spreadlock swaption but I don't find in the web any research article. Would you please provide me with some freely accessible papers on the web ? ...
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5answers
9k views

What is a regime switch?

I've come across the term regime switch in volatilities when reading about the modelling of interest rates but could not find a definition for a regime switch and what a regime is. Can somebody give ...
3
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2answers
1k views

Implementation of one-factor Hull-White short interest rate model

I am looking for implementation in R, VBA, C++, Python (or in any other programming language) of one-factor Hull-White short rate interest model according to the following article: Hull J. and White ...
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1answer
100 views

time step choice impact in Vasicek model simulations

I am trying to make some computations using Vasicek short rate model. Especially I a trying to compare exact expectation(obtained with the formula) and the expectation from Monte Carlo simulation. ...
9
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0answers
344 views

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 ...
3
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1answer
86 views

Ho & Lee yield curve fitting with zero coupon bond market prices

The Ho & Lee model for interest rates is given by the SDE: $$ \mathrm d r = \eta(t) \mathrm d t + c\,\mathrm d X $$ The calibration function for $\eta(t)$ is given by $$ \eta^*(t)=c^2(t-t^*)-\...
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1answer
104 views

a property of zero coupon bond in Brigo/Mercurio's “Interest Rate Models”

Let $P(t,T)$ be the the value of a contract at time $t$. This contract guarantees its holder the payment of $1$ at time $T$. consider $t<T<S$, when the interest rate is non-deterministic, do ...
2
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1answer
154 views

Construct a butterfly interest rate portfolio to eliminate PCA exposures

I have data from 2012 to 2016 for interest rates whose term range from 2 month to 30 years, a total of 10 Principal components can be calculated. Then I want to construct a portfolio, $$WFLY = w_1 *5Y ...
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2answers
609 views

Interest Rate Risk - The Greeks

IR Delta and Gamma. Can someone please explain if my understanding is accurate as relates to a 2yr interest rate swap? You are considered to be long Delta in an interest rate swap if you are ...
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0answers
28 views

Derivation of CIR interest rate model [duplicate]

I am trying to understand the derivation of the Cox-Ingersoll-Ross interest rate model. This has a stochastic differential equation of the form $$dr=(\eta-\gamma r)dt + \sqrt{\alpha r} \space dX$$ ...
6
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3answers
1k views

Why 10-year versus 2-year spread?

I occasionally see the 10y-2y spread referenced as a recession predictor. See, e.g., https://seekingalpha.com/article/4201787-current-slope-yield-curve-tell-us Why 10y minus 2y? Specifically, why use ...
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1answer
176 views

Why are interest rate swaps the most popular interest rate derivatives [closed]

Interest rate swaps are the most popular interest rate derivatives. Is there a reason why they are more popular than other interest rate derivatives (e.g. forwards, futures)? Is it because they were ...
7
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2answers
168 views

“Economic” Variables in Short Rate Models

Hull (9 ed.) states on p 707, "Equilibrium models usually start with assumptions about economic variables and derive a process for the short rate..." He then states the usual short rate models ...
4
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2answers
103 views

“Standard” Model for Effective Fed Funds Rate

Is there a "standard" model used to model the Effective Fed Funds Rate? I know that BGM is often used for LIBOR but haven't found a similar application to the Effective Fed Funds Rate. Do ...
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0answers
135 views

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....
3
votes
1answer
887 views

Why does one-factor short-rate model tend to produce parallel shift of the yield curve?

I understand that one factor short rate model models the instantaneous rate given any moment in time. Can anyone explain how to derive a term structure from a short rate model and show that one-factor ...
0
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1answer
128 views

What is the value/price of a bond paying floating rate

I am going through J.C.Hull for swaps. Where he says we can value a swap using bonds. Let $B_{fl}$: value of floating rate bond, $L$ notional principal. Why is $B_{fl} = L$ just after a payment ? What ...
2
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1answer
192 views

How are Interest Rate Swaps Quoted

Im not sure if this is the right place to ask this question or whether Personal Finance & Money would be a better place. Basically I know that initially interest rate swaps are quoted based on the ...
1
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1answer
91 views

Approximation of Forward Rates in discrete time

The forward rate from time $t$ to $T$ ($f_{t,T}$) can be approximated by: $$ f_{t,T}= \left[ \frac{(1+r_T)^T}{(1+r_t)^t} \right]^{\frac{1}{{T-t}}}-1 \sim \frac{(1+r_T)^T-(1+r_t)^t}{T-t} $$ Why is ...
2
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1answer
439 views

Relation between OIS rate and discounting rate

This is from book Modern Derivatives Pricing and Credit Exposure Analysis page 22 In an OIS, two parties exchange a fixed coupon (paid annually for longer-dated ...