I am trying to price callable bond with Hull trinomial tree. But the results i am getting are very dependent of choice of mean-reversion level. For testing purpose, i am using the same example as in Hull book, page 562: 10yr bond, flat 5% yirld curve, sigma=20%, 5%coupon semian., 1.5 yr call option with strike 105. mean reversion a=5%. With these setup, I got almost the same option value (0.67) as in book, but when i change mean reversion to 0.1, the option price is 0.41. Does it reasonable?And the second question is how to adjust tree to unequal time steps?thanks a lot!

can some one give me advise how to solve it, please......

nikki:i'll address your second question, since i haven't tested the exact params of that tree (but the numbers look fairly reasonable to me). to adjust a tree to unequal time steps, you need to decide if you want to fix the state space (i.e. the values your process can take) or the transition probabilities. I would suggest fixing the former, at least at first, as the process will be easier to understand. If this is the case, then you can just define a set of times t(0), t(1), ..., t(n). Just calculate the transition probabilities at each node according to the regular formulas but with delta_t = t(i) - t(i-1). note that you might get negative values for the transition probs, but that's an issue for another post.Sorry to be brief; if you need more help, let me know.

Thanks a lot for your answer, but unfortunately i can not change state space, my tree constror is not very flexible Can you tell me more about second option? thanks

my reply is for the case where you cannot change your state space.

what is the second way to do it anyway?thanks

but if we fix state space and change dt, will we still get positive probabilities? thanks

excuse my another silly question, how to incorporate time varying volatilities to HW tree?I am reading Schonbucher article "A tree inplementation of a credit spread model for credit derivatives" where he said that jmax >=0.184/(a*dt) is only true when vol is constant. And in case of time dependent vol j max is change at each time step, so probabilities will change too. I thought that probability actually independent from volatility, am i wrong?i really need you help, please.....