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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1answer
80 views

What is the Q-dynamics of affine bond prices when r is described by the given model?

Assuming an Affine term structure model, where bond prices arebe defined as: $$P(t,T)=\exp({A(t,T)-B(t,T)r_t)}$$ and describing the Q-dynamics of the short rate according to the Dothan model: $$dr_t=...
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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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1answer
71 views

Is the $NPV$ always a decreasing function in $r$

I was able to prove that, for positive Cash Flows $f_i$ and any value of $f_0$, the $NPV$ function is decreasing in $r$, hence, for $r_m<r_p=IRR$, then $NPV(r_m)>NPV(r_p)=0$. $$ NPV(r,f_i)=\sum_{...
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2answers
62 views

Calibrate Hull-white one factor model with swaption in analytical formula

I've been trying to calibrate Hull-white one factor model with swaption but I have a trouble making closed form solution of swaption Below is the part of paper I've been referencing to https://people....
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1answer
33 views

Implication of Humped Spot Curve on future spot curve(s)

I'm currently implementing a G++ model (Two Factor Hull & White model with constant parameters) on zero curve bootstrapped from USD IRS. Currently, USD IRS is humped at 30 years; swap rate goes up ...
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39 views

What is the correct volatility to use for inverting Black76?

I'm using VCUB on Bloomberg for ATM cap volatilities and have noticed there are a few "flavors" of volatilities. I would like simply use ATM flat vols to bootstrap forward volatilities from ...
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67 views

Which interest rate model is the most popular

Hey on wikpedia (https://en.wikipedia.org/wiki/Short-rate_model) there are quite a few short rate models listed, but which models are the most commonly used now? Because such simple models as Vasicek ...
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1answer
106 views

Hedging with FX swaps

I am trying to get the mechanic of the swap rollover. Funds usually hedge FX risk of their long term foreign assets (eg UST) with short term FX swaps (usually maturity < 1yr), by rolling over fx ...
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The Link Between Forward Rates and Randomly Generated Stochastic Rates

I'm reading about OAS models generated via Monte Carlo method. The method as described is that you generate simulate a bunch of interest rate paths for the 1 month rate. The text described 2 ways to ...
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4answers
167 views

Two practitioner questions about asset swap spreads

I have two questions regarding the terminology used on the practitioner side regarding asset swap spreads. Asset swaps are mainly used to retain the credit exposure of a bond while minimizing the ...
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0answers
35 views

Where can (current) interest rate cap prices be found?

I'm somewhat new to interest rate models and am interested in obtaining ATM cap prices and volatilities for calibration purposes (Black-Derman-Toy, Hull-White, etc.). Ideally, this would enable me to ...
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1answer
42 views

Bullet vs Monthly Loan (equivalent)

ive been working in a model to convert bullet loans to monthly paid (french) and the results seems to be ok but im not confortable with the results. If we compare both cash flows and discount every ...
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2answers
74 views

How is calculated the futures/forward convexity adjustment for FX?

I could find lots of stuff online for IR derivatives but it seems there isn't too much on FX for this specific adjustment.
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1answer
46 views

FX swap implied yield from bloomberg

I am trying to reproduce the bid EUR implied yield I see in the screenshot below for 1y tenor which is -0.6226%. EUR implied yield bid = spot_bid/fwd_bid *(1+i_USD_bid) - 1 Inputs from BBG terminal: ...
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31 views

Euribor + margin

I have this bond assigment where I have to calculate the CF each quarter, given a constant EURIBOR3M rate of -0,539%. There is also a 1,6% margin per annum that I have to take into account. The ...
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1answer
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Using compound interest rate in wrong way

I will explain the problem with an example. Today (14/03/2021) y agree a Zero-Coupon Mortgage with a nominal of a milion dolars an with an annual interest rate compounded annualy and with an ACT/360 ...
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1answer
64 views

Missing observations in ICE Swap rates

While searching time-series data for different interest rate benchmarks, I found that for the USD, all observations are missing for the period between March 2020/April 2020. This discontinuity is ...
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1answer
32 views

Why can a two-factor interest rate model not be used to value a coupon bearing bond as the sum of options on ZCBs

I am currently reading some notes which state that For one-factor models, the value of a European option on a coupon bond can be calculated as the sum of European options on zero-coupon bonds (ZCBs). ...
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35 views

Collateral and discounting of future cash flows

I am a beginner in this space and did some research on how the collateral posted affects the choice of the discounting curve in derivatives transactions. We have two scenarios based on the PV of a ...
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2answers
84 views

FX Forwards collateral and discounting

What is the market convention for discounting the future cash flows of FX forwards? In particular, I would be interested to know what discounting curves are used for both collateralised and not ...
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1answer
92 views

resettable/MtM cross currency swaps

I am trying to understand the mechanics of resettable xccy basis swaps and put together a numerical example. I'd like to know if 1) periodic interest payments are calculated on the original notional ...
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1answer
39 views

Can both good buying and good selling cause a bond to go special on repo?

A bond is known to go special when its repo rate gets particularly low relative to the GC (General Collateral) repo rate. In my mind, this can be caused by two scenarios: 1. Institutional interest to ...
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1answer
137 views

AUD funding rates

I am looking into into AUD rates and I am a little confused. I tried to summarise below my doubts. FX swap basis (difference between AUD FX swap implied rate and AUD OIS rate). Before covid-19 it has ...
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1answer
82 views

Fed fund market after QE

I read that before 2008, reserves of the banking system (vault cash and reserves at the Fed) fluctuated between \$40 billion and \$80 billion. However, as a result of quantitative easing, reserves ...
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1answer
45 views

Issue with Monte Carlo Simulation on an interest rate tree in Excel

I need to build a Monte Carlo simulation model that does 10 iterations on the interest rate tree. I need to identify the interest rate given a sequence of moving up and down the interest rate tree. I ...
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1answer
87 views

What are the practical costs of repo for a bond trading desk?

I appreciate what a repo/reverse repo transaction is, but I'm struggling to understand exactly how the cost of funding trades via repo works from a practical point of view for a bond trader. Current ...
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1answer
73 views

Australian banks funding

"Typically, Australian banks pay a small premium to swap foreign currency into Australian dollars. This premium is also referred to as the basis, which is the difference between the implied cost ...
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49 views

calculating risk free interest rate from put call parity

I'm trying to calculate the interest rate $r$ from the put-call parity. As per hull, put-call parity is given by the below equation. $c + Ke^{-rT} = p + S_{0}$ where: $c$ = current call option price ...
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60 views

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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124 views

Yield-to-maturity (YTM) vs effective annual rate (EAR)

If the yield-to-maturity (YTM) on a bond is 5%, is the effective annual rate (EAR) on the cash flows associated with the bond also 5%? I know that YTM does account for the present value of a bond's ...
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45 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, ...
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1answer
94 views

FX futures valuation under negative rates

Market participants use negative interbank rates (LIBOR JPY/CHF) for the valuation of FX futures. Does this make any economic sense? Positive rates in valuation formula indicate opportunity cost of ...
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0answers
28 views

Import an external term rates structure in QuantLib

I need to create a Monte Carlo simulation for a Hull-White process. I have the term rates structure already given in a csv, and imported it into Python with the name "rates". However, I have ...
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2answers
122 views

Carry trade question

Usually carry trades involve borrowing in a low yield currency and invest in a high yield currency. For example, I borrow dollars and invest in Brazilian real. I then use a rolling FX swap to hedge ...
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0answers
27 views

Swiss Central bank policy rate

I was wondering if the SNB as policy rate targets a specific level or sets a target range [upper bound, lower bound]. I look into this report from Credit Suisse and they mention the below on page 21. ...
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56 views

€str rates lower than ecb deposit yield

I have the following question : How can €str rate be lower than ecb deposit facility rates (deposit yield) ? Why would a bank lend money at that rate ? Thank you for your answers Edit : for instance ...
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0answers
50 views

Modeling overnight rates vs Central Bank benchmark using an Ornstein-Uhlenbeck model

I am working in a simple model for the overnight rate for an Latin American country(Chile). Currently the average overnight index trades around the benchmark rate set by the central bank(currently at ...
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1answer
48 views

Japan benchmark rates

Can you please confirm on the following? The difference between TONA (also called TONAR), JPY Libor, TIBOR is that: JPY Libor, TIBOR are based on quotes from panel banks. The difference between them ...
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1answer
59 views

Best way to lock in margin rate via hedging

I'm currently paying a 1.25% margin rate. This rate is based on the Fed Funds rate plus a margin. I would like to hedge against the possibility of this margin rate increasing. What is the best/...
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2answers
104 views

Risk-free interest rate for option pricing from treasury yield curve rates

I am experimenting with an implementation of the Black-Scholes valuation for call options, and ran into the following questions: Black-Scholes pricing requires a risk-free interest rate. What is '...
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0answers
31 views

Brazil FX market “cupom cambial” [duplicate]

I am trying to understand the role of cupom cambial (onshore dollar rate) in relation to the BCB swaps which are domestic NDF settled in real. "The cupom cambial is priced in basis points as an ...
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0answers
59 views

Implementation of solvers for curve construction

I'd be really interested to hear people's experiences of implementing global solvers for curve construction, especially with regard to how robust the approach is in practice, numerical performance, ...
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27 views

Interest rate futures notional

I was wondering what is the notional used to calculate tick values when the underlying of the futures is the average of an overnight rate (eg 1m SONIA futures, 1m EONIA futures, etc.)? When the ...
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1answer
50 views

Money market yield question

Assuming the 92-day and 274 day interest rate is 8% (act/360, money market yield) compute the 182- day forward rate starting in 92 days (act/360, money market yield). 1)7.80% 2)8.00% 3)8.20% 4)8.40% ...
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1answer
74 views

Are government bond yields usually expressed as yield to maturity (YTM) or annual yield?

If US 10yr = 2%, does it mean if I hold the bond until maturity/for next 10 years the yield is 2% or I get an annual return of 2% for 10 years? For example the yields in the link: https://www....
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49 views

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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23 views

Swaption model giving flat bachelier implied curve

I am working on interest rate models and was curious to Know if there exists a model giving a constant surface of implied volatilities. The implied volatiliy is taken as a normal (bachelier) ...
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24 views

Swaption with KO in FX

Curious to know if anyone has much experience modelling such products. I assume a three factor model (domestic/foreign interest rates/FX + correlation) would be necessary for these - but if the ...
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1answer
179 views

Gamma of interest rate derivatives

consider an interest rate derivative whose value $V$ depends on $n$ interest rates $r_1, \dots, r_n$. Hence $V$ is a function in $n$ variables $V(r_1, \dots, r_n)$. My question concerns the gamma $\...
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1answer
84 views

ECB - Two Tier System

It's said the theoretical aim of the ECB Two-tier system (exempt a portion of the excess reserves from negative rates) was designed to: offset the direct costs of negative interest rates on banks, ...

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