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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2answers
33 views

Why are interest supposed deterministic for equity?

I don't see why would rates be considered as deterministic when trying to price $\mathbb{E}^{Q} \left[ e^{-\int_{0}^{T_{f}}r_{s}ds} \left( S_{T_f} \right) | \mathcal{F}_{0} \right]$ I would like to ...
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Reconstructing bond proces with OIS rate

I am pricing derivatives under a $T$-forward measure and as such I need to discount the expected payoff with a bond price. I have available to me overnight-indexed swap (OIS) rates, how do I ...
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0answers
36 views

Use of Macaulay Duration to calculate the Funds Transfer Pricing Cost of an Amortizing Mortgage

I am asked to comment on the Funds Transfer Pricing methodology used by our Treasury to assign a Cost of Funds to a Loan. This is the current methodology: Let us say there is a 2 year loan with an ...
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4answers
119 views

Eurodollar future vs Eurodollar forward contracts

You are consider two contracts: a Eurodlloar futures contract with six months to maturity, selling at 5%, settled on three-month LIBOR, marked to market every day; and a Eurodollar forward contract ...
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1answer
46 views

Convexity of a rates Bermudan w.r.t strike

Recently there was a nice question asked on convexity of American put w.r.t strike: Convexity of an American put option Does the same hold for a Bermudan option in rates, where they underlyings are ...
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40 views

Pricing/Hedging a yield curve spread option (YCS)

I have 2 perspectives as to what model to use for a YCS option: It is an at the expiry option, so hit the marginals, correlate them with a copula, and be done with it. To hedge the vega, I will need ...
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1answer
57 views

How are SOFR futures contract quotes determined?

I am currently conducting a research on SOFR and have a small question. Suppose I am in June right now and on the CME website I see SOFR Futures quote for the month of September to be 98.6786. I wish ...
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1answer
82 views

Implication of forward-rate dynamics when the short-rate follows a normal process

In the section 3.2.3 of the second edition of "Interest Rate Models - Theory and Practice" by Brigo and Mercurio, the forward-rate dynamics implied by the CIR model is derived as follow: The ...
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1answer
58 views

Distribution and parameters for the amount at time T of Bond

An investor follows the following investment strategy from time t to time T: buys a 10-year zero coupon bond, holds it for a time-length dt, sells it and buys a new 10-year ZCB with the proceeds. The ...
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1answer
695 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 ...
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1answer
79 views

How would you use FRAs to find out how much Central Banks would cut/hike by?

Let's say you have The FRAs 1x4F, 2x5F, 3x6F, 4x7F, 5x8F... (meaning 3 months rate today, 3 months rate in 1 month, etc..) at 5.5, 5.5, 5.6, 5.55, 5.55. Assume today's date is 20/09/2019. You also ...
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1answer
70 views

Bermudan option exercise probability when rates rise

I am looking for an explanation of what happens to the Bermudan exercise probability (i.e. does probability of early exercise go higher if rates rise or lower) w.r.t rates. This is of course with ...
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37 views

Market pricing of forward US Treasury rates

What instrument(s) are used for forward pricing of US Treasuries? I know that Eurodollar futures are used for the market pricing of Libor in the future, but treasury futures only have contracts 3 ...
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1answer
128 views

Why is the numeraire in the LGM model tradeable?

I'm trying to understand the LGM model, which Hagan defines as follows. The state variable $X$ evolves according to $$dX(t) = \alpha(t) dW^N(t)$$ wrt the numeraire $$N(t) = \frac{1}{P(0,t)} e^{H(t)X(...
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3answers
156 views

How do we determine the “correct measure”?

Frequently I come across the statement that the "correct measure" for a product is this-or-that measure. For example, Eurodollar Futures or Stock returns - Risk neutral measure Libor forward rate - T-...
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1answer
38 views

Expected return rate greater than required return rate

I am a beginner to finance, today I found a question looks very simple that I am not quite sure about it. Question: Given I am paid \$50,000 now, growing at $6\%$ per year for a total of 10 years, ...
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1answer
31 views

Find the caplet volatilities for LIBOR fixings at each interval, given the ATM implied cap volatility term structure

anyone can provide solution or some idea to the following question? thanks
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0answers
63 views

Vega hedging swaption with caplets - precisely, what will go wrong?

I am trying to form a kind of unified perspective of how (vega) hedging an exotic with vanillas, or hedging a 'basket option' with vanillas will go wrong. So in particular, I want to be able to ...
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1answer
159 views

Modelling limitations and understanding of long term goverment bonds

Been trying to understand the yield curve for a while now. This is what I collected so far, There is a relation between short rates and long rates that goes via the forward rate, and so by the ...
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3answers
221 views

Python libraries for bloomberg?

I am very new with python, and I am used to work with bloomberg formulas for excel. I am starting to use a lot more python in my analysis, is there any library that performs same functions as bdp, bdh ...
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41 views

Martingale optimal transport

I'm a student and currently studying martingale optimal transport for deriving upper and lower contract bounds but i happen struggling on the fact that in most papers , interest rates are not taken in ...
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1answer
98 views

How to replicate the future instantaneous short rate?

Suppose we have an interest rate model $R(t)=\alpha(t)d(t)+\sigma d\tilde{W}(t)$, where the brownian motion is under the risk neutral measure. Suppose $S(t)$ is the price at time $t$ for a contract ...
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1answer
64 views

Market implied rate

Today's 3m usd libor (US0003M) is 0.3625% and 6m usd libor (US0006M) is 0.5484%, so from here, the implied 3m USD libor 3m forward is about 0.73%. Today's EDU0 quote is 99.71 (implied 0.29% rate). ...
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23 views

Calibrating Short-Rate Models to Eurodollar Futures Prices via Monte Carlo

I have a short rate model specified in the risk-neutral measure $Q$ defined by the continuously compounded money market $\beta(t)=e^{\int_0^tr(u)du}$. I'd like to calibrate this model to a set of ...
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0answers
21 views

Local v/s global calibration for a Bermudan Option (calibrate co-terminals vs entire matrix)

I am quite new to rates modeling and I have a question on the pros and cons of calibrating to larger set of vanilla instruments v/s calibrating to an exotic's 'natural' hedges. For example, I could ...
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1answer
112 views

Do different prices under different models admit arbitrage?

There are many models for interest rate. If two people use two different models to price the same interest rate derivative, and come to two different prices, doesn't that admit an arbitrage? How ...
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2answers
77 views

What is the best way to hedge a position with negative interest rate?

Suppose we have a following situation: $1).$ Company A takes a loan from Bank A at a floating interest rate. $2).$ In order to offset the payments at floating interest rate, Company A enters into an ...
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2answers
142 views

What does the word “affine” mean in affine term structure models?

I am new to the field of Mathematical Finance and wanted to get an idea on the intuitive, physical and mathematical meaning of the term "affine" in Affine term structure models. Any literature ...
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30 views

Sign of DV01 for FRA and IR Swap and Their Relationship

I'm confused with the sign notion (positive or negative) of DV01 for FRA and IRS. Say if I short FRA and also long IRS (pay fixed receive Float) with same underlying, does that mean both dv01 of these ...
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0answers
34 views

Trinomial Trees for Hull-White model

I am studying trinomial trees and trying to implement them in Python to compare them to the monte carlo simulation. I searched 3-4 hours in the web; but can't find any implementation on binomial or ...
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2answers
1k views

Libor Market Model Calibration

Currently I am doing a research on the plain vanilla multi-curve framework Libor Market Model meaning that no stochastic volatility is involved. I had the idea to calibrate to the swaption market. In ...
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1answer
65 views

Pricing coupon bond on weekly basis effectively

I have a coupon bond with $NV=20 000 000$ and coupon $4\% p.a.$, assumed the coupon is paid annually (I don't have this stated explicitly). Let's assume, the starting date is 27.4.2015, so the first ...
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1answer
149 views

daycount of the yield curve

Complete characterization of an interest rate requires a few elements: day count compounding frequency the rate itself start date and end date That said, I notice that day counts are never displayed ...
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1answer
79 views

When pricing interest rate swaps at inception, should the fixed rate or floating rate be priced first?

In an interest rate swap, when pricing at inception (e.g. making sure the NPV is zero at inception), is the fixed rate set first and then the floating rate calculated (or vice-versa, e.g. floating ...
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4answers
3k views

Where can I find open swaption implied volatility data?

Anyone have a good place to find interest rate swaption implied volatility data? Does Bloomberg's python API allow access?
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0answers
29 views

Excel rate function with nper as decimal returns unexpected result [closed]

I set up a simple problem Payment after 0.4 year is 25. The rate is 10%. I calculated PV as $\frac{25}{(1+10\%)^{0.4}} = 24.77$ Then I did Rate(0.4,25,-24.77,0) in ...
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1answer
90 views

impact of bond futures conversion factor on calendar spread trading

i have a quick question about conversion factor and his implication in calendar bonds roll trading. I go short on a calendar roll (short front+long back) which has the same cheapest to deliver. The ...
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2answers
223 views

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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1answer
94 views

Calculating risk free rates from risky options using put call parity

My questions relates to this post Implying risk-free rates using Put/Call parity , but I am using a different approach. Given: ODAX (Options on "DAX") Settlement prices across different maturities ...
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1answer
107 views

Formula for quantiles of swaprates in the 1-factor Hull-White model

Is there a closed formula to approximate the quantiles of swaprates in the 1-factor Hull White model? Background The Hull-White is a Gaussian model for the short rate. Its mean and covariance ...
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1answer
43 views

Why is CBS (Currency Basis Swaps) added to Interest Rates?

We are trying to analyze an algorithm (internal to our company) to calculate currency option pricing using the Garman and Kohlhagen model. Our internal algorithm calls for CBS (Currency Basis Swaps) ...
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1answer
46 views

Valuation of a REPO

I thought I had a pretty good grasp on how to calculate this but I'm getting questioned on it and just want to be sure I'm not getting it mixed up. In my notation you enter into the repo contract at $...
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2answers
93 views

Bootstrap zero curve source of information

I'm trying to understand the bootstrap methodology to construct a zero curve from a par curve in detail. I'm looking for a good source of information, preferably with a detailed example, that ...
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1answer
63 views

Calculating the daily continuously compounded return from index values

Given I have 3 index values at time $t = 0, 1 , 2$, how would I go about calculating the daily continuously compounded return? Time: $ 0, 1, 2$ Index Values: $4000, 4086, 4114$ Any help would be ...
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1answer
75 views

Normal vs. Lognormal Greeks for Negative Rates Options

My understanding is that for some of the G10 currencies with negative rates (CHF, EUR), Swaption and Cap / Floor prices are quoted in terms of BOTH, normal and log-normal Vols. That in itself is not ...
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1answer
85 views

Is this regression suitable for fixed income products (negative interest rates)?

I am currently looking at a regression which tries to model EWMA volatility in the presence of negative interest rates. The regression is as follows and uses absolute return instead of relative in ...
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2answers
701 views

Why Markov Functional Models (Hunt 2000) are not yet so popular?

I refer to MFM introduced by Hunt [2000]. These models can be seen a subset of interest rate market models. MFM allow us to describe the term structure elements using a set a functions of a low-...
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37 views

Resources to calculate EIR

I'm looking for resources on calculations of effective interest rate across different kind of financial products like bond, term loans, etc. Thanks!
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1answer
31 views

Compute Forward Exchange Rates using Risk Free Rates

In the following image : I am not able to understand how, the final value of strategy B can be equal to $e^{r_{GBP}T}F(0,T)$ According to me it should be just $F(0,T)$ My reasoning is that when you ...
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0answers
65 views

What are reset periods/dates in relation with interest rate swaps?

Let's assume I have a 2-year fixed-floating swap, the floating leg has a quarterly reset. Does this mean the valuation is done every 3 months for the floating leg? (and the total value of these 4 ...

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