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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21 views

Does the solution to this problem on floorlets have an error?

I'm self-studying and encountered the below problem and solution. I believe the payoff of the put at node $dd$ would be $(1.044)^{-1}\max(0.05 - 0.02, 0) = 0.019157088,$ and similarly the payoff at ...
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40 views

How inplement monte carlo simulation in bdt model ? (interest rate)

I want to implement monte carlo method in Black–Derman–Toy model to preview short interest rates. $$d\ln r_t=(\theta_t+\frac{\sigma'_t}{\sigma_t}\ln r_t)dt+\sigma_tdW_t$$ Someone can explain what ...
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28 views

Modelling nominal interest rates

What is the best model for nominal interest rates? ARMA, VAR, VEC, FAVAR, etc? I am a R user, so please advise me the most convenient R package to use as well. I intend to model US nominal interest ...
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1answer
55 views

Swaption pricing

I am trying to understand the pricing of various types of swaptions. Suppose I have a swap that starts in 3 months time. How would I go about pricing a swaption on this swap in the following cases: ...
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44 views

Code for quasi-Gaussian model (Cheyette model)

I'm looking into the quasi-Gaussian model with linear local volatility as explained by Andersen and Piterbarg (Interest Rate Modeling, Volume 2). I'm trying to calibrate this model and implement it. I ...
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25 views

Model free estimation of convexity in Eurodollar IR Futures

Can someone please share some thoughts on how to estimate convexity for a given Eurodollar interest rate future contract, without assuming any underlying model for rates i.e. LMM, Hull-White etc. I ...
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1answer
92 views

stochastic interest rate $r_t=x_t+y_t$

Let $$dr_t=(\alpha(t)-\beta r_t)dt+\sigma dW_t$$ where $\alpha$ is non stochastic process and $\beta$ and $\sigma$ are constant. Can we write process $r_t$ in the form $$r_t=x_t+y_t$$ where the ...
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1answer
85 views

Bond price under Poissonian model of interest rate

Working through an exercise in interest rate modelling and I have the following setup: $r_t = r_0 + \delta N_t$ where $\delta > 0$ and $\lambda > 0$ is the intensity of the Poisson pricess $N_t$...
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1answer
80 views

How to measure the real interest rate using the consumer price index

I am examining how investor sentiment affects the probability of stock market crises. I am using methodology similar to this paper https://ideas.repec.org/p/dij/wpfarg/1110304.html. One of the ...
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2answers
79 views

Does LIBOR in USD reflect short term interest rates in the U.S.?

The London Interbank Offered Rate (LIBOR) is an indicative average interest rate at which a selection of banks (the panel banks) are prepared to lend one another unsecured funds on the London money ...
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43 views

Using CME DV01 to predict Futures price at 0.00% Yield

DV01 is published at CME Group for the cheapest-to-deliver bond here: http://www.cmegroup.com/trading/interest-rates/invoice-spread-calculator.html. If my goal is to get an approximation where the ...
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31 views

Introducing 1bp shocks to yield curve (and interpolation consequences)

Let us assume we have a LIBOR 3M curve and that I would like to introduce a small shock up/down of 1bp at a certain point along the curve. I am trying to find out what the best and most efficient way ...
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62 views

Exploding Libor Rates in Libor Market Model

I have implemented the Libor Market Model in Matlab. When I generate a number of paths, I notice that some of them explode. Does anybody have an idea what could cause this? I already tried solving ...
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1answer
90 views

What if: Negative interest on an overdrawn bank account?

Theoretical question: Consider if a bank account had a -12% yearly interest rate, and an account was currently overdrawn to a balance of -$100. What would the bank do to the -$100 balance after one ...
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1answer
54 views

Why does the correlation between r and V in Longstaff and Schwartz 1992 model is positive?

I am reading the Longstaff and Schwartz's 1992 and 1993. From $r = \alpha x + \beta y$ and $V = \alpha^2 x + \beta^2 y$. It was mentioned in the paper that the $r$ is positive correlated with $V$. ...
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1answer
86 views

Valuing derivatives under stochastic interest rates

I would like to price a European option with maturity equals to 5 years. To do this, I'm using the Black-Scholes model with stochastic interest rates. Suppose I choose the CIR model for the risk-...
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1answer
76 views

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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39 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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22 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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1answer
78 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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2answers
84 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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22 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 cost/...
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1answer
42 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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1answer
68 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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2answers
63 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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2answers
116 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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1answer
104 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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1answer
68 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
93 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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1answer
64 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 $$P(t,T)=e^{A(t,T)-B(t,T)...
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1answer
97 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 $C_{BS}(F_0,K,T,\...
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2answers
99 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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68 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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1answer
66 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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1answer
78 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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23 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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2answers
43 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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2answers
50 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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0answers
13 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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19 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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0answers
57 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 ...
2
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2answers
163 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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1answer
30 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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35 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
84 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 ...
3
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2answers
84 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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1answer
85 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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1answer
66 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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22 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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1answer
88 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 ...