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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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How does the interest rate affect the implied volatility of options, especially ITM?

What would be a good reference to understand how the interest rate (r) or dividend yield (q), and I guess the differential between the two, affect the implied volatility of the options? If I look at a ...
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Euribor 3M simulation

I am required to simulate the trajectory of the Euribor3M rate as it is crucial for determining the future cash flows of my derivative instrument. I've received guidance to employ the Hull-White model....
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2 answers
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Mathematical meaning of an inverted yield curve

I am currently working on rates model. I would like to understand, mathematically, what does it mean to have an inverted yield curve? And I am asking myself for a certain model, how can I generate an ...
StochasticMan's user avatar
1 vote
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Multiple factor Hull-While and yield curve deformation

I am currently studying rate models and I understand that the One-Factor model has some incompleteness: The yield-curve can only be shifted. But I don’t understand what parameter controls this shift ( ...
Adel Chakir's user avatar
2 votes
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101 views

Measure of the behavior of Swaption surface

I'm looking to find a different measure than average shift move to explain the behavior of the IR VOL products say Swaption. I know it's a very open question not only touching upon IR VOL scope. Let ...
Michael W's user avatar
3 votes
1 answer
304 views

Model-free convexity adjustment

I have the settlement prices of 3-month SOFR IMM futures and I'm trying to compute the forward curve to replicate FactSet's results, but I have trouble understanding how they do the convexity ...
Katie's user avatar
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7 votes
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Recent developments in interest rate modelling

Brigo and Mercurio published the 2nd edition of their (classic? definitive?) book on interest rate models in 2006. Have there been any major theoretical developments since then? Has anyone published a ...
Jamie Ballingall's user avatar
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Pricing with log-normal interes rate

The annual rate of return in year $t$, denoted as $1+i_t$, where $i_0$ represents the interest rate from $t=0$ to $t=1$, has a log-normal distribution with an expected value $108\%$ and a standard ...
Miłosz 's user avatar
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Potential Future Exposure for vanilla swap

I need to calculate the PFE for vanilla swap. I wonder if it makes sense to simulate the MC scenarios with a 1-factor Hull white model. In my opinion, this model only allows parallel curve ...
SIMO's user avatar
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Risk free rate for Black and Scholes model: Incorporating inflation?

I am new to quantitative finance and I am trying to create a model for option pricing. Naturally the Black and Scholes equation is front and center for this sort of thing, but that raises the question ...
SSC Fan's user avatar
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2 votes
1 answer
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Why does the risk-free rate implied by put-call parity vary with strike prices?

Suppose I do the following: buy one lot of some underlying stock currently trading at price $S$, write a call with strike price $K$, earning some premium $C$, and buy a put with the same strike $K$, ...
Jérémie Koenig's user avatar
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What book/resources would you recommend for beginners in IRD? [duplicate]

I recently graduated with a MS degree in Quantitative Finance and will presumably have some work to do with Interest Rate Derivatives (IRD) in the future. Since my experience lies more in the equity ...
Gull23's user avatar
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2 votes
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Interest rate derivatives market data - download [closed]

EDIT; I looking for sources where from I could get interest rate derivatives market data? (caps,floors,swaptions, etc, is there data available for exotics ones or are they purely OTC?) I would grade ...
Dar12342's user avatar
5 votes
0 answers
63 views

Separability of Stochastic Volatility Model

After having read the article of Trolle & Schwartz regarding their general stochastic volatility term structure model (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=966364), it is not clear ...
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Any other ways to hedge a bond portfolio against interest rate risk? [closed]

I'm currently taking a (gentle) intro to derivatives class. One of the exercises asked me to discuss duration as a risk measure and to provide alternative methods of hedging a bond portfolio against ...
l337n00b's user avatar
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Approximating implied price vol from implied yield vol?

I am wondering if there are any approximations that exist to convert yield vol to price vol? I am dealing options on SOFR futures, which can be quoted in yield and price (i.e. 3% put and $97 call are ...
Zac Likes Vol's user avatar
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26 views

Barrier Reverse Convertible on interest rate

I'm trying to find the price of an barrier reverse convertible on interest rate - https://structuredproducts-ch.leonteq.com/isin/CH1251797945. I have simulated the underlying interest rate by Vasicek ...
ballastexitenz's user avatar
1 vote
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425 views

Fitting volatility using SABR

I have been working on generating a volatility surface for options on SOFR futures with the help of the SABR model. I am running into some trouble for low strikes in particular, in that I cannot seem ...
Zac Likes Vol's user avatar
1 vote
0 answers
64 views

I am trying to compute the the tail of a future roll using the ratio of forward dv01

I am trying to compute the the tail of a future roll using the ratio of forward dv01, per the link CME: Calendar Spreads with Tails : I am trying to compute the the tail of a future roll using the ...
viki's user avatar
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Vasicek model calibration to bond prices or rates (no swaptions)

I need to calibrate Vasicek's model $dr_{t} = a(\theta - r_{t})dt + \sigma dW_{t}$ in a market with no swaptions. I was thinking in estimating $\sigma$ with historic data, but I'm in the doubt with ...
Oliver Mohr Bonometti's user avatar
1 vote
0 answers
213 views

Determining the floating rate for an interest rate swap

I'm trying to price an Euribor 6M Swap and comparing this to Bloomberg's swap manager. However, I'm having some doubts on my implementation of getting the reset rate for the floating leg. In Bloomberg ...
aghilario's user avatar
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98 views

Lend $ synthetically at higher yield using ¥: it works but why?

The Trade is: You have USD 100m funding Swap USD for YEN equivalent at today's spot, agree to swap back in 12 months at the USD/JPY forward rate With the YEN buy a 12 months Japanese Government bond ...
tweedi's user avatar
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1 answer
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Quantlib FRA and interpolated rate in Swaps vs BBG valuation

I am building a CZK swap pricer on quantlib, and I am trying to understand my differences with Bloomberg pricing. I believe the way I set up my FRA is wrong, the reason is because even though I match ...
Gloomy's user avatar
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How to convert the parameters of multi-factors cheyette model (quasi-Gaussian model) from tenors to factors?

The book "Interest Rate Modeling" by Andersen and Piterbarg is an extermely fascinating book on interest rate derivatives. Recently, I have encoutered some issues while reading this book. ...
Yong-guang Gong's user avatar
1 vote
1 answer
259 views

Quantlib - mismatch with BBG Swap

I'm trying to price a CZK swap via Quantlib with BBG data, so far nothing complicated but I can't seem to match the floating leg cashflows, and NPV, when I price my swaps, even if I find the right Par ...
Gloomy's user avatar
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1 answer
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Are there any structural reasons for choosing constant forward rate interpolation over linear interpolation beyond just simplicity?

I've been looking into rate curve interpolation methods and focussing on two basic ones - linear interpolation, and constant forward rate interpolation. In the first one, given a rate curve consisting ...
Charlie Shuffler's user avatar
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1 answer
726 views

PV01: bumping all tenors along the curve or only a tenor at a time?

Item 22 from this ISDA SIMM 2.3 document gives the following definition for the PV01 of an instrument $i$ with respect to the tenor $t$: $$s(i, r_t) = V_i(r_t+1bp, cs_t) - V_i(r_t, cs_t)$$ where $r_t$ ...
SuavestArt's user avatar
0 votes
0 answers
47 views

Interpolating FRA curves for MPC dates

I have data for all the "white" FRAs with 3m fixings in a given market, i.e., 1x4 up to 9x12 and all the central back MPC meeting dates over the next twelve months. What is the recommended ...
Vladimir Nabokov's user avatar
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40 views

CMS diffusive dynamic

As I am landing on a project related to CMS option, I am wondering if one can write dynamic for CMS depending on the pricing model. For example, is it possible to have a diffusive dynamic for the CMS ...
StochasticMan's user avatar
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48 views

Trinomial lattice model movement probability calculation under various models

I need to construct trinomial lattice model movement probability calculation under various models Vasicek, Hull White, Ho Lee and Hull White Two Factor. I do not see any reference to these models with ...
P RAY's user avatar
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1 answer
223 views

Deriving central bank hikes/cuts from a swap curve

Can you please explain the following? Please assume I am 5 years old. how do you derive the cuts/hikes of the policy rate priced in a swap curve? why you can derive the cuts/hikes only from a swap ...
Finance_student's user avatar
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0 answers
211 views

Pricing a callable bond in a minimal way

I am looking for a minimal way to price callable bond from a defaultable issuer. The idea is to assume that we are in a deterministic world (i.e no volatility). I tried a methodology but I am not sure ...
mazalaza's user avatar
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0 answers
292 views

Bootstrapping overnight SOFR rates from futures

I'm struggling with the best way to approach bootstrapping out a SOFR curve using SOFR 1m and 3m futures. Theoretically, unless I'm wrong, there should be a way to price out the expected overnight ...
Tom's user avatar
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0 votes
1 answer
221 views

Effect on Forward Swap Rate from a parallel shift in forward curve

Can anything be said on how a parallel shift in the forward curve affects the forward swap curve? To be more concise, say we have a model estimate of the implied vol for the 2Y-10Y point (2Y ...
J Muscat's user avatar
0 votes
0 answers
76 views

Kalman Filtering to estimate parameters of G2++ Model

I'm trying to use Kalman Filtering to estimate the parameters of the G2++ short rate model. For this, I've been using Implementing Short Rate Models: A Practical Guide by F.C. Park. For reference, he ...
Pudge Superior's user avatar
1 vote
0 answers
102 views

For which interest rates r is the model arbitrage-free?

Given $\Omega=\{\omega_1,...,\omega_4\}$ and a probability measure $\mathbb{P}$ on $(\Omega, \mathcal{P}(\Omega))$ where $\mathbb{P}(\{\omega_i\})>0$ for all $i$. Let, furthermore, $r\geq 0$, $S_0=...
Analysis's user avatar
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2 votes
0 answers
157 views

How do forward-looking forward rates in the Mercurio's and Lyashenko's normal or extended FMM model represent EURIBOR rates

(By XIBOR I intend any EURIBOR or LIBOR rate. By RFR I intend SOFR for the USD and ESTR (€STR) for EUR.) I am mainly focused on the EUR rates market (but also a bit on the USD market) and looking for ...
Olórin's user avatar
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A rates model for EUR and USD pricing in different underlyings (EURIBOR (yes) or ESTR, and SOFR)

Being a house mainly focused on almost everything else that rates products we never had a "rates pricer", no surprise. The best connected to rates thing we have is an equity/fx/what have you ...
Olórin's user avatar
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0 votes
0 answers
202 views

How to hedge 3 Month SOFR futures with 1 Month SOFR futures considering FOMC meeting

Has anyone considered trading SR3 vs SR1 SOFR futures? They both have the same underlying basis of daily SOFR, and how would one calculate a hedge ratio for the SR1 to trade along SR3? Looking at the ...
Borla312's user avatar
2 votes
0 answers
82 views

ATM cap prices in Vasicek model (Filipovic)

I am trying to replicate the ATM cap prices in table 7.1 (see bottom of this post) from Filipovic's book "Term Structure Models - A Graduate Course" which assume the Vasicek model and uses ...
Landscape's user avatar
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1 answer
531 views

Carry for an Interest Rate Swap

I don't get why for calculating the carry of a spot starting swap I need to adjust the difference between the fixed rate and fixing by the Dv01? For example if I receive in a 5y swap and want to ...
Finance_student's user avatar
2 votes
0 answers
117 views

Cheyette Model vs Markov Functional Model

Just like to understand more about the model difference between 1d-Cheyette Model vs 1d-Markov Functional Model. Is there a model difference betweeen these 2?
Benedict's user avatar
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0 votes
2 answers
1k views

How to calculate YTM in case coupon payments are reinvested at a different rate than the bond's coupon rate?

I know that calculations of yield to maturity(YTM) assume that all coupon payments are reinvested at the same rate as the bond's current yield and take into account the bond's current market price, ...
catGPT's user avatar
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2 votes
1 answer
149 views

Recommended books/resources for IRRBB risk metrics calculation

Any recommendations for books/resources/videos/on-demand courses for in-depth IRRBB-related risk metrics calculation etc? Yield Curve Risk, Basis Risk, Repricing Risk, Optionality Risk, Value at Risk, ...
Pat's user avatar
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3 votes
1 answer
634 views

Curve construction with Python's RATESLIB package

As per the user guide of Python's RATESLIB package (https://rateslib.readthedocs.io/en/latest/i_guide.html#guide-doc), below example is provided to construct a Curve ...
augustine's user avatar
0 votes
0 answers
53 views

Simple short rate model that generates ZCB skew

Which is the simplest short rate model that generates ZCB vol skew ? I want to use it afterwards and do simple "on paper" qualitative development about its dynamic(I don't need a model I can ...
stackoverflower's user avatar
2 votes
2 answers
156 views

Forward interest rate curve family parametrization

There are many academic sources, books and articles, introducing forward interest rate curve. For example, those authors define $f(\tau)=f(\tau;\beta_0,\beta_1,\beta_2,\lambda)$ as a function of time ...
Vnature's user avatar
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1 vote
0 answers
179 views

How can I use Monte Carlo to price a Zero-coupon bond in the Cox-Ingersoll-Ross model?

Let me prefix this by saying that, yes, Cox-Ingersoll-Ross (C.I.R.) is deprecated when used to model interest rates. Yet integrals of the form $$P(0,T) = E\left(\exp\left(-\int_0^Tr_s ds\right)\right) ...
Martin Erhardt's user avatar
2 votes
0 answers
92 views

Black-Karasinski & Market Price of Risk [closed]

I have implemented the Black-Karasinski model using trinomial trees and calibrated following Brigo (2007) page 29. However, the results do not fit the interest rate curve practiced in the market. As I ...
user3081005's user avatar
3 votes
0 answers
227 views

How to calculate spot rates using market data of bonds?

Given 3 Bonds $A$, $B$ and $C$ with \begin{matrix} & \text{Bond } A& \text{Bond } B& \text{Bond } C& \\ \text{Price:}& 101,12\%& 99,03\%& 102,95\%\\ \text{Mat. in years:}&...
julian2000P's user avatar

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