# hullwhite

### interest rates - Black Derman Toy model: from tree to differential equation

From the gentleman and scholar Emanuel Derman. Emanuel states "the last two pages answer the question asked". https://www.dropbox.com/s/cg299qsbquuqdru/TwitterNotesOnBDT.2017.pdf?dl=0&m= Please thank... Read More

### risk management - Hull White help needed

On the Monte-Carlo Simulation of the Hull-White Model : You can find the specification of the Euler Scheme simulation in https://ssrn.com/abstract=2737091 . The paper gives the exact Euler step, i.e.... Read More

### simulations - Calibration of 1F Hull White short-rate model to market data

Suppose we have a set of $NT$ maturities $\taut$ and a set of $Nk$ strikes $Kk$ .For each maturity-strike combination $(\taut,Kk)$ we have a market price (for example) $Caplet(\taut,Kk)=C{tk}$ and a... Read More

### derivatives - On short-rate-models: Black-Karasinski (with constant parameters) compared to Vasicek

I will refer to "Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit" by Damiano Brigo and Fabio Mercurio. In chapter 3 (One-factor short-rate models) they have a very nice... Read More

### hullwhite - 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)} r_... Read More

### hullwhite - Calibration of Hull White One factor model in F.C.Park paper

That's right. Calibration is done in other to obtain one 'a' (mean reversion rate) and one sigma for the entire curve. This case is referred to as the Hull White model with constant mean reversion, i... Read More

### Applicability of PCA to get historical volatilities to calibrate interest rates trees

The first principle component of interest rates will not help you capture the term structure better at all. It will basically remove all term structure affects you are going to see. When we decompos... Read More

### interest rates - Time dependent parameters in Hull-White model

On your first question , the fact that you fit to the yield curve $-$ which is what the standard Hull-White model with time-dependent $\theta(t)$ allows to do $-$ does not mean that you are fitting t... Read More

### Hull White Stochastic Volatility Model in Matlab

In order to compute $$P0 = \mathbb {E}[C (\hat{V})]$$ where $$\hat{V} = \frac {1}{T} \int0^T \sigma^2s ds$$ and $$d\sigmat = \sigmat (\alpha dt + \gamma dWt)$$ using Monte Carlo, you should: G... Read More

### stochastic calculus - Extended Hull White Interest Rate Model for Zero Coupon Bond

Here is a solution without using the PDE technique, which is preferred as we do not need to assume the affine form of a zero-coupon price from the start. we assume that, under the risk-neutral measur... Read More