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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57 views

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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82 views

Cross currency swap basis with USD added on the covered interest rate parity (CIP)

We know the adjusted covered interest rate parity (CIP): $$Forward = \dfrac{1+r\cdot\tau+b}{1+r^*\cdot\tau+b^*}Spot$$ Here $r/r^*$ is the risk-free foreign/domestic rate and $b/b^*$ is the cross ...
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37 views

Term structure model for exchange-traded STIR futures and their options

As I understand, models such as the SABR extension of the Libor Market Model are the "standard" for interest rate derivative valuation in OTC markets, where options tend to be European and it is ...
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1answer
165 views

Why financing costs are ignored in capital budgeting of projects?

Any finance textbook I have encountered including CFA materials states something like this: "Financing costs are ignored. This may seem unrealistic, but it is not. Most of the time, analysts want to ...
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1answer
115 views

Calculation of Combined IRR

How to calculate combined IRR for two different cost of funds? The emi (Equated Monthly Installment) amount, whether it is calculated separately or based on the combined IRR should be same. I tried ...
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248 views

Calculating spot rates from forward rates

I am working on a problem where I am trying to calculate the forward rates from two different spot rates. I have the following: ...
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1answer
48 views

Continuously Compounded rate less than a discretely compounded rate [closed]

I'm looking at an example in a well known book and its saying "consider an interest rate that is quoted as 10% per annum with semi annual compounding" The book puts 10% as the semi-annual rate, ...
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37 views

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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32 views

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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1answer
132 views

Ho-Lee short rate model under the Heath-Jarrow-Morton framework

Under the Heath-Jarrow-Morton (HJM) framework the dynamics of the Ho-Lee short rate model are defined as following: $$dr(t)=\theta(t)dt+\sigma dW^{\mathbb{Q}}(t)$$ with $\mathbb{Q}$ the risk-neutral ...
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85 views

Why are KRDs calculated by shifting the par curve?

When we compute Key Rate Duration, why is the par curve the right curve to shift instead of the spot curve?
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1answer
96 views

How to calculate Spot Rate with interest rate [closed]

You are a foreign exchange trader specialized in the US dollar Swiss franc market (USD/CHF). One morning, you notice that the one-year dollar interest rate is 4%, while the one-year interest rate on ...
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243 views

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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1answer
139 views

What's the difference between instantaneous forward rates and observable forward rates?

Source: http://docs.fincad.com/support/developerFunc/mathref/LIBORMarketModel.htm "In contrast to models that evolve the instantaneous short rate (Hull-White, Black-Karasinski models) or ...
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59 views

How is a LIBOR Market Model volatility skew determined?

LIBOR based interest rates are derived from the prices (supply / demand) of swaptions, caps and floors. These prices are generally quoted in yield vols. Their prices are given by the Black formula. ...
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91 views

how to simplify Inflation year-on-year option to Zero-coupon option

Belgrade 2004 paper basically proposes that inflation year-on-year volatilities (and hence yoy options) are basically the spread vols between the Zero-coupon vols from (t0 to T) minus the zero-coupon ...
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70 views

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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1answer
115 views

Deriving interest rate term structure in a short rate model

I have often seen a statement that we can model only a short rate process $r(t)$ and then use it to derive a term structure $R(t,T)$ for every $t$. Could someone please elaborate? Say, I’ve simulated $...
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121 views

Short rate models

On the short rate model in Wikipedia https://en.m.wikipedia.org/wiki/Short-rate_model Why is the first function, the P(t,T) given? This is not the short rate model this is generating prices for a ...
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1answer
117 views

Interest rates, effect on call price

Generally, we assume that an interest rate increase makes the call price more expensive. From my understanding it is because the expected return on the stock price increases. However the interest rate ...
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127 views

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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2answers
866 views

Quantitative strategies in the Fixed Income space

I'm looking to learn more about systematic strategies in the the fixed income space, particularly in Rates products (anything from simple cash to inflation or vol). I've been reading a couple of ...
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1answer
896 views

Quantlib-Python: use zero rates to get the originally bootstrapped curve

Let's say I am trying to build a curve using deposits, future and swaps with one of the three Quantlib methods in Python as below: ...
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2answers
312 views

OIS, Fed Funds Rate and Working

I'm a bit confused about OIS. Is OIS the overnight interest rate or is it a swap. If OIS is the rate at which banks lend overnight, where does the swap come in? Don't they borrow at a fixed rate? ...
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2answers
247 views

Application of Itô's lemma - Forward process

How would be applied the itô's lemma in the following equation: And we know that:
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36 views

Calculating the interest portion of a loan between two dates

The IPMT function in Excel calculates the interest portion of a loan between 2 dates. Is this a closed loop formula? Or are the payments projected and the interest summed up? I need to implement ...
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80 views

Forward rate versus 10 year constant maturity swap

In Yield Book, the cashflows are projected using the current coupon + a spread on the 10 year constant maturity swap How is this 10 year constant maturity swap different from the forward rate curve? ...
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1answer
91 views

What's the difference between the short rate model projection and the 3M forward curve?

A term structure has a forward curve So what is it that the short rate model is projecting exactly? Why is it needed? How are they different?
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66 views

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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304 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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83 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 ...
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1answer
64 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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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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66 views

Cash vs Deposit Rates

When constructing a yield curve for derivatives purposes, what is the difference between cash and deposits rates?
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1answer
752 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% ...
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1answer
729 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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1answer
604 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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99 views

Curve Building + Swap Pricing [duplicate]

Assume Swap means a USD Swap with standard conventions (semi-annual fixed payments and quarterly floating payments, etc).
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354 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
362 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 ...
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1answer
1k 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 ...
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1answer
193 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 ...
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56 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 ...
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4answers
604 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 ...
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1answer
106 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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265 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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84 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 ...
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129 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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108 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. ...
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426 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 ...