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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Price compounding: Swap versus Governments Bonds

There are different rates curve to compound prices. Since the crisis, regulators tends to favor price compounding with swap curves over IR curves deduced from governments bonds (EU regulators, french ...
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45 views

To calculate shift in the shifted lognormal model

I tried to calculate the shift for CHF interest rates (tenors with negative rates) using MLE, but as the shift is increased the MLE value increases(or decreases depending on whether positive or ...
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52 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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27 views

Different ways to discretize forward rate in HJM

I've come across couple of different ways to discretize the forward rate equation in HJM. If somebody could please help me understand why is it possible to have multiple ways here and how to pick up ...
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24 views

Data on interest rate differentials (lending on own vs. foreign currency)

I'm looking for data on (inner country) interest rate differentials between lending in own and foreign currency. Is there any data publicly available? If yes, where? If not, which non-free sources are ...
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1answer
96 views

Monetary Policy and the Yield Curve PART TWO

The Fed has a number of tools/targets with which they manage monetary policy. I'm looking to refine a concise summary of them and looking for guidance/correction/validation. Think I understand these ...
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57 views

Monetary Policy and the Yield Curve PART ONE

As I understand it, the Fed has 3 tools for moving interest rates to combat inflation/unemployment: the discount rate, Fed Funds rate and open market operations. I'm trying to understand how the ...
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64 views

How was this probability of negative U.S rates by end 2017 calculated?

http://www.bloomberg.com/news/articles/2016-01-26/bets-on-negative-u-s-rates-by-end-2017-jump-above-10-chance Options markets show some investors are taking out protection in case rates instead ...
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58 views

“Spot rate is not observable” meaning

In Bruno Remillard's text, "Statistical Methods for Financial Engineering," he states the following on p 148 after giving the general form of a bond price $P(t,T)$ under Vasicek's model: Note that ...
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70 views

State of Art - Nelson Siegel Modeling

My idea is to work with dynamic Nelson Siegel models(DNS) on my master's thesis. As I am finishing undergraduation this year I started researching on the subject. I wonder what is being discussed in ...
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62 views

Fed Funds Rate - why has it just started decreasing on the final day of each month (vs quarter)

I understand why the Fed Funds rate has historically dropped on the final day of each quarter, but in 2015 it appears that the effective Fed Funds rate now drops on the final day of each month as ...
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57 views

Will rolling-down-yield-curve bond strategy work if interest rates remain unchanged?

Suppose I have 2 strategies; A) Buying A One Year Bond And Holding To Maturity (Buy & Hold To Maturity) B) Buying A 3 Year Bond and Selling After One Year (Rolling Down The Yield Curve) Assume ...
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104 views

Function A(t,T) in one-factor Hull-White model

I am struggling with Hull-White model now and have the following question: in the lecture notes under the link below I see how A(t,T) and B(t,T) are being derived. This requires the solution of ...
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163 views

Historical calibration of Hull-White model

I have a question concerning 1-factor Hull-White model. For my master project I need to calibrate it to compute Counterparty credit risk metrics. I know that the model might be calibrated either for ...
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1answer
253 views

Weights Blowing up in PCA

I'm using daily settlement data to get yield levels for a couple of products. From this data I am doing PCA on a rolling collection of the yield levels. I have been using sci-kit learn's PCA function, ...
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139 views

Monte Carlo, convexity and Risk-Neutral ZCB Pricing

I've built a simplistic Excel monte carlo model to price a zero-coupon bond, but it came up with a slightly unepxected result so I wanted to confirm whether my maths is just a little rusty or my model ...
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29 views

Calculation of bond spot rates [closed]

the cash prices of six months and one year treasury bills are \$120 and \$115 respectively. A 1.5 years bond that will pay coupons of \$5 every six months currently sells for \$121. A 2 years bond ...
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26 views

Why the growth of the American Economy is going to cause the Fed to raise interest rates?

Due the growth of the American economy the Fed have published that interest rates are likely to increase. Why is that the response of the Fed?
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102 views

Hot do I calculate an effective forward rate? [closed]

I have to find nominal and effective forward interest rate for 3M-9M term, knowing that current interest rates are: 3M - 2.05% 6M - 2.04% 9M - 2.03% 12M - 2.02% For a nominal interest rate I just ...
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45 views

Pricing inflation lags

I've been looking into a short piece of maths I found on pricing inflation with payment delays, and was hoping someone could confirm whether my understanding was correct or if the maths isn't quite ...
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160 views

Incompatibility of Lognormal Forward Model (LMM\BGM) and Lognormal Swap Model

In his paper On the distributional distance between the Libor and the Swap market models (and also in his book about IR modeling) D.Brigo says: 10, 11, 12 are defined in the end of message. Do I ...
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115 views

How to convert HJM model risk-neutral measure $\mathbb{Q}$ to real measure $\mathbb{P}$?

HJM model, $df(t,T) = \mu(t,T) dt + \xi (t, T)dW(t)$, is defined in risk-neutral measure $\mathbb{Q}$, according to Brigo's "Interest Rate Models" book. I wonder, how could I transform it to real ...
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157 views

What's the link between EURIBOR3M futures volatility and rates volatility?

If I am not wrong, EURIBOR3M futures with maturity $T$, whose price is $F_{T}$, are quoted like contracts which express the underlying forward rates, $r_{T}$, as $$r_{T}=\frac{100-F_{T}}{100}$$ Now ...
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86 views

How do bond futures affect effective rate when used to hedge a bond's duration?

I'm trying to wrap my head around what happens to the net interest received when an invester goes short a bond future to fully hedge the duration of his long position in an actual bond. Does it ...
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83 views

Neglect the positive values in negative interest rates modelling?

The magnitude of the negative interested rate should vary correlated with the increase in fixed assets prices and with cross-currency basis spreads. Could their volatility / correlation ...
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79 views

Separated software and physical cash flows modelling and pricing to be used with negative interest rates?

The physical cash presence in the final transactions is one of the issues in the presently observed negative interest rates bonds. Such a situation has historically been modelled within the "liquidity ...
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122 views

What is the meaning of the discounted process defined from the interest rate process?

Assume a money market has interest rate process $R(t)$. In Shreve's Stochastic Calculus for Finance II, formula (5.2.17) on page 215 defines the discounted process as $$ D(t) = e^{-\int_0^t R(s) ds}. ...
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77 views

Accuracy Rebonato Swaption Approximation Formula among Different Strikes

Can somebody explain me if the Rebonato swaption volatility approximation formula is accurate for only ATM strikes, and if yes why? Can it also be used for ITM and OTM strikes? My foundings: Let $0 ...
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2answers
57 views

Pricing a physical commodity forward contract

I have just started reading Options Volatility and Pricing 2nd edition and I'm a little confused on forward contract pricing. The book states ...
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54 views

Ho-Lee model - A and B derivation for $P(t,T)=e^{-A(t,T)-B(t,T)r_t}$

I am analyzing the transition of the bond prices in the affine models in the form of $P(t,T)=e^{-A(t,T)-B(t,T)r_t}$ using the property that the diffusion and the drift of an affine model can be ...
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2answers
48 views

Can we derive 5 year zero coupon interest rate by using 1, 2 and 3 year zero coupon interest rate?

Given that the 1 year zero coupon bond interest rate is 5%, 2 year zero coupon bond interest rate is 6% and 3 year zero coupon bond interest rate is 7%. 4 year coupon bond price and interest rate are ...
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43 views

AUD Swap Reference Rate?

So I understand that BBSW is the reference rate used in AUD swap transactions since AUD LIBOR has been discontinued. If I want to build a curve out of the reference rates used to price AUD swaps, I ...
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93 views

Price of an equity

An equity has a value of 100 Euros, and pay a dividend of 5 Euros in 6 months. The interest rate of 6 months is 5% and the interest rate for 1 year is 6%. I would like to compute the value of the ...
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30 views

Equitable Allocation

This questions borders on the actuarial side of things but the general solution should have relevance in several situations. Suppose we have a set of $k$ people who will retire in $\{n_1,...,n_k\}$ ...
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1answer
49 views

Interest Rate and Price of Assets

I have a very basic question about finance. I know that for an asset, the price is inversly related to the yield to maturity, or the interest rate. However, I have three ways of thinking about this ...
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2answers
100 views

Reproducing levels when PCA has been done on changes

I want to use PCA for rich/cheap analysis of interest rates. For this I did the PCA on the time series of daily difference in interest rates, which is stationary. I cant do pca on levels, as they are ...
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308 views

Bootstrapping zero-rates from AUD swap rates

I have a pay fixed / receive floating interest-rate-swap on the AUD BBSY that I'd like to price for the purposes of accounting. I understand the general process to be as follows (assuming ...
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186 views

Derive instantaneous forward rate

Given that $P(0,T)=e^{-RT}$, how does one get the formula for the instantaneous forward rate below? Specifically, how does one get to the partial derivative in the formula? I'm sure the answer is ...
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1answer
643 views

Zero Curve Calculation for AUD, CAD (post LIBOR scandal)

In the end of May 2013 British Bankers Association (BBA) stopped publishing LIBOR rates for Australian and Canadian dollars in a light of recent scandals. LIBOR rates were essential for creating zero ...
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69 views

Relationship between interest rate and corporate bond yield?

I have been reading articles on liability driven investing, a technique used to increase the correlation b/w assets and liabilities of a pension plan. It appears that they use AA rated corporate bond ...
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63 views

Kalman Filter in Interest Rate Models

A couple questions regarding the use of Kalman filtering in estimating parameters of short rate models: 1) In Duan & Simonato (1995), which seems to be one of the earliest applications of the ...
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41 views

Swaption on a swap with 0 year tenor

Any ideas on valuation of IRS swaption on a swap with 0 year tenor? As an example, we have a 5 year swaption, on expiration it is cash settled; the underlying swap tenor is 0 years with excercise and ...
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76 views

can an fx forward price simply be divided into 1 to quote the inverse?

Qu 1. Say I ask for EURUSD 1 week and get prices: 1.120986 / 1.120216 Does that mean to price USDEUR 1 week I can divide 1 / 1.120216 and 1 / 1.120986 and get rates: 0.8921 / 0.8927 Or is that ...
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1answer
117 views

Bond price in Ho-Lee Model

I know Ho-Lee model and want to extract the price at $t$, of a European call option with strike price $K$ and exercise date $T$, on an underlying $S$-bond, but I don't know what way should I choose: ...
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1answer
47 views

How do I interpret yield curve data points given by the US Treasury?

Given the Daily US Treasury Yield Curve Rates for a specific date I will fit the curve with the cubic spline method, but first I need to know how to use the data points given by the Treasury. For ...
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853 views

What is the difference between BBSW and AUD LIBOR?

I understand that BBSW is the reference rate for financial instruments while AUD LIBOR is the interbank rate benchmark. However, since AUD LIBOR has been discontinued due to the rigging scandal, can ...
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437 views

Hedging future USD cost using different IR and forwards

I am facing a problem where I suppose an expense in 6 months from now of 2,500USD. My home currency shall be EUR, and I am trying to hedge given the following information. ...
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428 views

Non-intuitive correlation between S&P sector indexes and economic indicators

I am trying to understand how changes in economic indicators like Unemployment Rate, Inflation Rate, and Consumer Sentiment affect the portfolio values. For that I want to measure the correlation ...
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2answers
434 views

Matlab; How to specify Coupon frequency for Interest Rate Swap

I'm trying to price an interest rate swap and would like to change the default coupon payment frequency from 1 a year to 2 or 4 a year. I'm using ...
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29 views

Pricing back swaptions corresponding to underlying swaps of Bermudan Swaption in calibrated LMM

I do not know to which swaption volatility matrix I have to calibrate the LMM in order to price back correctly the swaptions corresponding to the underlying swaps of a Bermudan Swaption. My problem: ...