Questions tagged [bdt]

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61 views

Issue with Monte Carlo Simulation on an interest rate tree in Excel

I need to build a Monte Carlo simulation model that does 10 iterations on the interest rate tree. I need to identify the interest rate given a sequence of moving up and down the interest rate tree. I ...
2
votes
0answers
70 views

Arrow Debreu Price vs Green's function

How is the Arrow Debreu Price related to Green's function at an intuitive level and how is this used in practice? Note Added 2021/02/01 I came across this in the Black Derman Toy model paper by Boyle, ...
2
votes
0answers
76 views

Zero Coupon Volatility data

I am trying to construct a Black-Derman-Toy trinomial tree as explained in Espen Haug's Complete Guide to Option Pricing Formulas, chapter 11. Where do I get the Inputs (table 11-2) from if I wanted ...
1
vote
0answers
77 views

Relation between BDT volatility and Hull-White one factor Volatility

Is there any mathematical relationship between the volatility of spot rates calibrated from Lognormal model and the volatility of spot rates calibrated from HW one factor model?
2
votes
2answers
2k views

How to express the Black Derman & Toy Model in a $dr=A\,dt+B\, dW$ form?

The Black Derman & Toy (BDT) model is given by $$d(\ln\,r)=\left(\theta(t)-\frac {d(\ln\sigma(t))}{dt}\ln r\right)\,dt+\sigma(t) \, dW.$$ How can one rewrite the BDT model as $dr=A\,dt+B\, dW$, ...
16
votes
2answers
1k views

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

My question in short is as follows: can I take main principal component of historical covariance matrix and use it as historical volatilities when fitting a binomial tree? Here's more detailed ...
4
votes
2answers
2k views

BDT model implementation

I am looking for a nice and readable description of how to implement BDT model: $d log(r(t)) = [\theta(t)-\frac{\sigma'(t)}{\sigma(t)}log(r(t))]dt + \sigma(t) dW$. I assume I already have steady-...