# Tag Info

Accepted

### How to get set the theta function in the Hull-White model to replicate the current yield curve

Concerning your first question, this depends on what curve, currency, etc. you are interested in. The general method for constructing yield curves is called bootstrapping which allows you to derive ...
• 8,089

### What is the purpose of short rate models?

Short rate models were first used in the 1970s and 1980s to try to fit and explain the term structure of interest rates - they went beyond simple parametric shapes (polynomials and exponential forms). ...
• 2,167

### Why isn't the Vasicek model arbitrage-free?

Short rate models are broadly divided into equilibrium models and no-arbitrage models. The models from Vasicek, Dothan and Cox, Ingersoll and Ross are examples of equilibrium short rate models. The ...
• 16k
Accepted

### Differences between main classes of interest pricing derivatives models

I am not sure if you can classify it like that. Mind you, I never wrote a book. I'll write what I know below and you can decide if the classification makes sense or not. 1 ) STIR: as the term ...
• 8,969
Accepted

### Problem with pricing a call option using the Monte Carlo Vasicek model

To make sure that I understand the problem: you are trying to price a call option expiring at time 0.5, which will exercise into a unit notional zero-coupon bond with a maturity of 1.0 at a strike (...
• 845
Accepted

### QuantLib Gsr model

the model is described in Andersen, Piterbarg: Interest Rate Modeling. The formulas that are acutally implemented are derived here https://ssrn.com/abstract=2246013 Best Peter

### Ho Lee model in Baxter&Rennie

Here we provide another answer using Ito's calculus. It appears involved, but it also has its own interest. Given the short rate dynamics \begin{align*} dr_t = \nu(r_t, t) dt + \rho(r_t, t) dW_t, \...
• 21.1k
Accepted

• 741
Accepted

### Variance of the Cox-Ingersoll-Ross short rate

The independence assumption is not needed. In fact, based on Ito's isometry and the Fubini theorem, \begin{align*} Var(r_t) &= E\left((r_t-E(r_t))^2 \right)\\ &=\sigma^2 e^{-2\beta t} E\left(\...
• 21.1k
Accepted

• 741
Accepted

### QuantLib - Calibrating Hull White one-factor on negative interest rates

When building a SwaptionHelper, you have to tell QuantLib what kind of volatility you are inputting. There are three options: Black Vol, Shifted Black Vol and Normal Vol. Since you don't have black ...
• 5,825
Accepted

### Affine Structure Resolution for the Vasicek model

We begin with the equation $1+B_t(t,T)-kB(t,T) = 0 \quad(1)$ \begin{align} (1) & \iff e^{-kt}+e^{-kt}B_t(t,T)+(-k)e^{-kt}B(t,T) = 0 \\ & \iff e^{-kt}+ \frac{\partial}{\partial t}\left(e^{-kt}B(...
• 1,008
Accepted

### Calibration of Heston model with stochastic short rate

If we take your model literally (with the correction that I suggested as a comment), then there exists no (semi-)closed form, IMHO, that you can use for asset pricing. What you could do is then to ...
• 6,673

### Why should future short rates tend towards the current term structure of interest rates?

It really depends for what purpose you are using the model. Letâ€™s say you are using it for valuation of some instrument. If you want the fair market value, then a) is irrelevant and you would instead ...
• 17.2k

### what's the difference between instantaneous short rate and instantaneous forward rate?

In more standard notation the instantaneous forward rate is written as $f(t,T)$, that is, the continuously compounded interest rate seen at $t$ for the infinitesimal interest period $[T,T+dt]\,.$ ...
• 2,033
Accepted

### Difference HJM Framework versus Short rate model

Most principal component analyses (PCAs) on historical data of yield curves find that typically a yield curve moves parallel flips from normal to inverse (or vice versa) twists (changes its ...
• 2,033
For any given process for the short rate $\{r_t,, t >0\}$, the price at time $t$ of a zero-coupon bond with maturity $T$, where $t\le T$, is given by \begin{align*} P(t, T) = E\left(e^{-\int_t^T ...