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

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

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

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

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

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

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

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

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

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