### Chap.8, pb 4

Posted:

**Tue Oct 05, 2010 10:01 am**This problem deals with binary tree construction given time-dependent volatility.

The issue here is to determine the vector of times so that we get the same fraction of total volatility at each time step. Given a general volatility parameter, the obvious approach seems to use a solver to find the time t such that the integral of variance from the previous time step to t matches a given volatility value.

Using for example a simple dichotomy solution, this slows down considerably the contruction of the BinaryTree object, at least for the vector of discounts. This even if it is done only once (for each set number of steps).

But the use of solvers is only detailled in the following chapter, not a this point. Is there any other valid approach to that problem?

By advance, thanks for your answer.

The issue here is to determine the vector of times so that we get the same fraction of total volatility at each time step. Given a general volatility parameter, the obvious approach seems to use a solver to find the time t such that the integral of variance from the previous time step to t matches a given volatility value.

Using for example a simple dichotomy solution, this slows down considerably the contruction of the BinaryTree object, at least for the vector of discounts. This even if it is done only once (for each set number of steps).

But the use of solvers is only detailled in the following chapter, not a this point. Is there any other valid approach to that problem?

By advance, thanks for your answer.