Lower one year rates

[Soccerboy]

There is a fomula that goes like this..the one for generating interest rate trees

RL = Ro * e^(-2 * sigma)

RH = Ro * e^(2 * sigma)

for a 1yr jump..What happens if we have a half year jump?, do we multiply the Exponent by a factor of say 0.5 for half year jump, ie will:

RH = Ro * e^(2 * sigma*0.5)?

Thanks

[AG]

You're mixing the oranges with the apples.

"up" = r0 * exp(sigma x (root t))
"down" = 1/"up"

This holds for one binomial model. The relation of RL to RH is another binomial model.

[Kenny]

To continue AG's explanation

R_H = R_L e^(-2 * sigma)

where R_L will be given. The lowest rate in any given time period will be given and the "higher" rates can be determined using the above equation.

[J-Man]

Not necessarily. You might have to calibrate the tree.

[Tim><]

Originally Posted by J-Man

Not necessarily. You might have to calibrate the tree.

Doubtful for any period beyond year 1. For year 1, f1 should equal the average of rh and rl.

Regarding the underlying question though, if annual volatility is sigma, this is really saying that annual variance is sigma squared. Consequently, semiannual variance would be 1/2 sigma squared. Semianual volatility would be 1/sqrt(2) sigma.

[Car'a'carn]

Originally Posted by Kenny

To continue AG's explanation

R_H = R_L e^(-2 * sigma)

where R_L will be given. The lowest rate in any given time period will be given and the "higher" rates can be determined using the above equation.

You probably meant it this way:

R_H = R_L e^(2 * sigma)

[Kenny]

Originally Posted by Car'a'carn

You probably meant it this way:

R_H = R_L e^(2 * sigma)

Expecting me to remember more than one thing correctly in a day sure is asking a lot

[Still_On_Diet]

Originally Posted by AG

You're mixing the oranges with the apples.

"up" = r0 * exp(sigma x (root t))
"down" = 1/"up"

This holds for one binomial model. The relation of RL to RH is another binomial model.

r0 is what?
does this model hold for interest rates too? I have seen this model (with root t) only for stock prices..