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 to build a cross currency swap pricer?

We're looking to build a pricer to convert a funding spread in a given currency over a specific funding basis e.g. 20 bps EUR 3m€ and convert it to a funding spread to a different currency with a ...
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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: ...
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16 views

Are forward rates starting at observation date spot rates?

In part 3.2 of Lu and Neftci (2003) "Convexity Adjustments and Forward Libor Model: Case of Constant Maturity Swaps", the authors propose a new way of pricing CMS swaps, with Monte Carlo simulations. ...
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44 views

How can extract parameters in the CIR model from data?

I want extract CIR parameters from monthly LIBOR data in the EULER-MARYAMA method in MATLAB languge. I find data but I cant extract parametrs form that! what is the process? what is the formula?
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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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19 views

Modeling the distrubution of future swap rates

I'm interested in better understanding the unwind cost/value of a swap at various points in the future. Suppose that we have entered a 7Y swap (paying fixed) and want to understand the unwind ...
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19 views

Impact of the interest rate volatility in the valuation of a bond

I am currently valuating a bond whose cupons have the following structure: $\left\{ \begin{array}{rcl} H_j-2\% & \mbox{if} & R_j<H_j-2\% \\ R_j & \mbox{if} & H_j-2\%\leq R_j\leq ...
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63 views

HJM framework problem - showing that HJM drift condition implies that $b(z)=b+βz$ and $(ρ)^2=α$

Hi I am looking for some general clarification to Heath–Jarrow–Morton framework. I am analyzing a problem where the forward rate is modeled as $$ f(t,T)=e^{\beta(T-t)} Z_t+h(T-t) \tag{1}$$ for some ...
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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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94 views

CIR model problem - deriving PDE, Feynman-Kac

I am reviewing a CIR model problem, where $r_t$ has following dynamics $$dr_t=a(b-r_t)dt+\sigma \sqrt{r_t} dW_t^* \quad \quad (1)$$ for some constants $ab>\frac{\sigma^2}{2} \quad$ Letting T ...
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50 views

LIBOR 3M and 1M from Vasicek model

I would like to discuss my approach toward modelling of interest rates with respect to its downsides and advantages. My problem is to forecast daily LIBOR 3M and LIBOR 1M over a particular time ...
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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
81 views

How to show that the exponential Vasicek model is not an affine term-structure model?

From the pricing formula, we know that the value at time $t\in [0,T]$ of a zero coupon bond maturing at time $T$ is $$ B(t,T)=E\left(\exp{\left(-\int_{t}^{T}r_sds\right)}\bigg|\mathcal{F}_t\right). ...
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53 views

Vasicek model problem

I am analyzing a problem where the below is given Vasicek model with risk-neutral dynamics $$dr_t = \kappa (\theta - r_t)dt + \sqrt{r_t} dW_t \quad \quad (1) $$ bond prices ...
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41 views

SABR Calibration: Normal vs Log-Normal Market Data

This question is about getting some clarification as to how to understand market quotes for normal & log-normal vols together with certain model assumptions. So let us define ...
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2answers
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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60 views

Interpolation of forward zeros-coupons bonds simulations for missing maturities (ESG data)

I have a set of economic scenarios simulated with Barrie and Hibbert ESG. The stochastic model for interest rates used is Libor Market Model Shifted. I am facing a problem with zeros-coupons prices. ...
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35 views

shifted SABR - ATM vol

quick question guys. I know that for Shifted SABR (or any other Shifted model), we simply model the underlying price process (lets say the forward interest rate F), as F' = F + x, x being the shift. ...
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53 views

Pricing a Vanilla swap between coupons; What rates to use?

Vanilla Swap question. Entered into a 5Y fixed for floating HUF swap. Fixed is annual coupons, Float is semi-annual coupons. 1 month later I want to price it. I set up my future values for Fixed ...
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20 views

Why does the forward rate curve lies above the spot rate curve and the yield to maturity curve?

I saw a picture of 3 different yield curves, a spot rate curve, a forward curve, and a yield to maturity curve. The forward curve was at the top, the YTM curve at the bottom. I don't understand why.
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42 views

Integration to calculate expected value of swap rate

In Hagan's paper on valuing CMS swaps (Convexity Conundrums: Pricing CMS Swaps, Caps, and Floors), there is: So the swap rate must also be a Martingale, and $$E \big[ R_s(\tau) \big| ...
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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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12 views

EMTA Guidelines

Does EMTA guidelines are only for Non-Deliverable trades? IF yes, then why this is applicable for Deliverable Option trades? EMTA Site - http://www.emta.org/ndftt.aspx
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15 views

Forward Exchange Rate Data: Germany x US

Would anyone know where I can find historical forward exchange rate data between germany and US, yen and US to download? In Bank of England website i already found. Thanks
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53 views

Modeling Interest-only Mortgages

First post on this forum - happy to be here. Please give feedback if this is off-topic so I can more meaningfully contribute moving forward. Can we infer a range of future all-in costs for I/O ARMs ...
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126 views

How to price a stock under Q and stochastic interest rates?

I am interested in pricing a stock under $\mathbb{Q}$ when I assume that $$dS(t) = \mu(S(t))dt + \sigma(S(t))dW(t)$$ where $W(t)$ is a Wiener process under $\mathbb{P}$ and $$dr(t) = a(b-r(t))dt ...
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24 views

how to compute the risk free rate for a given maturity of an option contract?

i'm working on options with different maturities. I need to correspond a risk free rate for each maturity. What rate should i consider as risk free rate? thank you.
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34 views

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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1answer
70 views

How to calculate the NPV (Net present Value) in this question? [closed]

A company pays £1,200,000 to purchase a property. The company pays £30,000 at the end of each of the next six months to renovate the property. At the end of the eighth month the company sells the ...
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79 views

How to calculate interest rate in this problem?

Problem: A loan of £12,000 is issued and is repaid in instalments of £300 at the end of each month for 4 years. Calculate the effective annual rate of interest for this loan. What I tried- But ...
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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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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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21 views

Principal Components based term structure and stochastic market price of risk

Suppose I would like to define an affine term structure model for interest rates using the 3 principal components of level, slope and curvature. Then if I would like to add a stochastic market price ...
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76 views

How do you model yield curves for interest rates that have hardly moved?

I have a model which I use to simulate future yield curves. The model uses some standard concepts, like PCA and ARMA models, and it creates some nice-looking yield curves. The simulated curves are ...
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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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2answers
99 views

Derive an expression for the value of the asset as a function of time, V(t), t>=0

An investor deposits USD 300 in a bank account at time 0, reinvests all interest payments and continuously invests USD 300 per annum, until the total value of the deposits reaches USD 3312. At that ...
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1answer
109 views

Consequence of negative mean reversion of hull white one factor model

I tried to calibrate the data for hull-white one-factor model. Sometimes, I get negative estimate of mean reversion factor after the calibration process. When I plug the negative mean reversion factor ...
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33 views

Reset Date standard for ICP (Indice Camara Promedio) trade

What is the Reset Date standard for ICP (Indice Camara Promedio) trade? Trade Currencies are USD v/s CLP. Please provide the ISDA link if there are any amendments to ISDA standards.
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38 views

Can I use these rates for ACT/360 discounting?

I have calculated forward rates like this: $r_{t_1,t_2} = \left(\frac{(1+r_2)^{d_2}}{(1+r_1)^{d_1}}\right)^{\frac{1}{d_2-d_1}} - 1 $ I want to find the discount factors for these forward, with ...
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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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32 views

positive financial leverage in real estate

I had the understanding that leverage always helped improve cash on cash returns so long as the interest paid was less than the unlevered rate of return/cap rate. doing a quick back of the envelope ...
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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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25 views

Calibration of Dothan Model to Yields

For both the Vasicek and CIR model the yields $R(t,T)$ and short rates $r_t$ have an affine relationship: $$ R(t,T) = \frac{B(t,T)r_t - A(t,T)}{T-t}, $$ where $A(t,T)$ and $B(t,T)$ are determined by ...
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126 views

What is drift in interest rate term structure model

I was studying about the interest rate term structures and i came across term structure model with (and without) drift. I am really unsure about what this drift is in this equation for term structure ...
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36 views

Analytical Bond Price under Rendlemen-Bartter?

Assuming the short rate $r_t$ follows the risk-neutral (so $W_t$ is a $Q$-Brownian motion) process $$ dr_t = ar_t dt + \sigma r_t dW_t, $$ does anyone know of an analytical bond price formula? We ...
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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 ...
4
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138 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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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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45 views

For a square-root process (CIR), how to verify the characteristic function of the transition density?

I am trying to solve a financial mathematical question. I derived PDE (a) for the characteristic function as follows. But, I don't know how to verify the following characteristic function of the ...
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87 views

Ridiculous Bond Prices under Vasicek Model

Has anyone played with the parameters of the Vasicek model and observed the sometimes ridiculous bond prices it implies? E.g. with the right parameters, a 30-year zero is priced at $147,327. To be ...