Path-dependent deals are typically priced by Monte Carlo, which is easy to be implemented but suffers low speed and inaccurate greeks. On the other hand, tree/grid based methods are fast and can result in stable greeks. Is it feasible to price path-dependent callable deals on the tree/grid. Many thanks.

barrier options can be priced on a grid and they are path dependent. cliquets i'm not so sure.callable CBs can be priced on a grid.give us a specific structure.

You can price everything with a non-recombining tree... but complexity is of the order of 2^n...

QuoteOriginally posted by: eiriamjhYou can price everything with a non-recombining tree... but complexity is of the order of 2^n...Use FDM, it's easier to program than a non-recombining tree and more stable and accurate. Question: what is meant by order 2^n?

> cliquets i'm not so sure.I thought I saw an FDM scheme for these on Wilmott jrnl. recently, I think by Paul himself.

> Question: what is meant by order 2^n? In a non-recombining tree (which is what you need for a heavily path-dependent derivative) you have 2^n nodes at the n-th steperstwhile gave examples of light path-dependent derivatives which can be priced in a standard recombining tree (or, better, finite differences on a grid)e.

QuoteOriginally posted by: eiriamjh> Question: what is meant by order 2^n? In a non-recombining tree (which is what you need for a heavily path-dependent derivative) you have 2^n nodes at the n-th steperstwhile gave examples of light path-dependent derivatives which can be priced in a standard recombining tree (or, better, finite differences on a grid)e.This number seems to be very big. I have not programmed this kind of structure but with a FDM with J and N subdivisions in S and t we need at most (J+1) * (N+1) mesh points.When you say heavily PD, do you mean 1-factor barriers and Asians, or two-factor ones? By the way, FDM can handle any derivative that has a PDE (based on SDE for the corresponding underlying). Are you discrete monitoring as well? Remark: what is a typical value of n in 2^n? I's kind of mind-boggling but I suppose I am missing some essential insights. Is this the 'exploding bushy tree' property?I have wriiten an article on barriers, with some typical results (FIRST article in the series) http://www.datasim-component.com/financ ... =resources regardsDD

Here at XYZ LLP we use a price farm of 100 BlueGene/L's, and it takes only 1 nanosecond to price a 10Y American double-barrier lookback with conditional cap/floors and discrete and continuous monitoring using a non-recombining tree.......Obviously non-recombining trees are computationally expensive, so you cannot implement this method in full with a lot of steps... My remark was more theoretical than practicale.

I don't understand what is so difficult about using a recombining tree. It seems to me that by adjusting u/d/p at each node, even with an arbitrary local deterministic volatility, it should be possible to build a set of nodes at each level, suitable for any path-dependent condition. What sort of path-dependent conditions would make this difficult?

QuoteOriginally posted by: eiriamjhHere at XYZ LLP we use a price farm of 100 BlueGene/L's, and it takes only 1 nanosecond to price a 10Y American double-barrier lookback with conditional cap/floors and discrete and continuous monitoring using a non-recombining tree.......Obviously non-recombining trees are computationally expensive, so you cannot implement this method in full with a lot of steps... My remark was more theoretical than practicale.It would be interesting to compare to FDM solution.Two questions:1. What kind of datastructure do you use?2. As Fermion also asks, what is the precise nature of the problem? IR option? So it's just 1 factor?

QuoteOriginally posted by: FermionI don't understand what is so difficult about using a recombining tree. It seems to me that by adjusting u/d/p at each node, even with an arbitrary local deterministic volatility, it should be possible to build a set of nodes at each level, suitable for any path-dependent condition. What sort of path-dependent conditions would make this difficult?Consider the middle node of a 2-step binomial recombining tree. How do you know if you arrived at this node with an up-down path or a down-up?There are tricks to get around this problem but they are payoff-specifice.

QuoteOriginally posted by: eiriamjhConsider the middle node of a 2-step binomial recombining tree. How do you know if you arrived at this node with an up-down path or a down-up?There are tricks to get around this problem but they are payoff-specificWell, I've not yet done any work on path-dependent contracts (other than American exercise) so I don't know much about this, but for what sort of contract would knowing the path probabilities not be sufficient?

> for what sort of contract would knowing the path probabilities not be sufficient? e.g. callable note where the coupon formula depends on average performance of the underlying?

Ok, I see the problem. Thanks.

the standard way to price path-dependent things on a grid/tree is to use an auxiliary variable.see wilmott's book for asian options, or see my book