# Tag Info

Accepted

### Hull-White formula on wikipedia, correct?

For the Hull-White model, where \begin{align*} dr_t = (\theta(t)-a r_t)dt+ \sigma dW_t, \end{align*} under the risk-neutral measure, we have that, for $t\ge s \ge 0$, \begin{align*} r_t = e^{-a(t-s)} ...
• 21.2k
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 ...
• 8,119
Accepted

• 2,023

### Hull-White model: match between HJM framework and short model formulation

Note that \begin{align*} f(t, T) = f(0, T) + \int_0^t\alpha(u,T)du+\int_0^t\sigma e^{-a(T-u)}dW_u, \end{align*} where, based on this question, \begin{align*} f(0, T) = \int_0^T \theta(u) e^{-a(T-u)} ...
• 21.2k

### Current discount rate of Hull White One-Factor Monte Carlo Simulation

The average of simulated discount factors from the Hull-White model and market discount factor are the same in theory but very similar in the simulation due to numerical error. I draw one figure ...
• 41
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 ...
• 5,835

### 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
Accepted

### Derivations of the pricing PDE for the Heston-Hull-White or Heston-CIR models

Let's consider the following dynamics under a risk-neutral measure:\begin{align} \text{d}S&=(r-q) S \text{d}t + \sqrt{v} S \text{d}Z_S,\\ \text{d}v &= \kappa_v (\theta_v - v) \text{d}t + \...
• 16k