Questions tagged [bdt]

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Black-Derman-Toy model AND European-type bond call option

In a Black-Derman-Toy model in which Ω ={ ω1, ω2, ω3, ω4 }, the risk-neutral probability for each state ωi, i = 1, 2, 3, 4 is 1/4 . The spot rates in BDT model are given as follows. ω r1 r2 ...
2
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0answers
71 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
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44 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
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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
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2answers
955 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
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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-...