Recombining trees

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Recombining trees

Hi Dr Joshi
I have been working on your paper Acheiving Higher Order convergence for the prices of European options in Binomial trees.
While proving corollary 3.3 about final layer how can we find all the nodes in the final layer by moving up or down from the central node.
Plz guide me in this regard.
Moreover how can we say that in the final layer the total number of nodes will be even in case of recombining trees defined for odd number of steps.
kindly guide.
memonasif

Posts: 4
Joined: Fri Jun 24, 2011 8:38 pm

Re: Recombining trees

the number of nodes in the final layer is the number of steps +1
mj

Posts: 1380
Joined: Fri Jul 27, 2007 7:21 am

Re: Recombining trees

Ok I got it. but what about the nodes in the final layer which you say in the paper can be found by moving up or down from the central node in the previous layer.How can we get all the nodes in the final layer by moving up or down from the central node in the previous layer.
Please guide me in this regard.
Moreover what do you mean by the trees are centred on K(Strike Price).
memonasif

Posts: 4
Joined: Fri Jun 24, 2011 8:38 pm

Re: Recombining trees

if you allow several moves you can get to all the nodes in the final layer from the middle one on the previous layer.
mj

Posts: 1380
Joined: Fri Jul 27, 2007 7:21 am

Re: Recombining trees

Well, Dr Mark Joshi could you please let me know what do you mean by the trees are centred on K(Strike Price).
either you mean that in each time steps the central node will be equal to the strike price K or you mean something else.
plz guide.
memonasif

Posts: 4
Joined: Fri Jun 24, 2011 8:38 pm

Re: Recombining trees

mj wrote:if you allow several moves you can get to all the nodes in the final layer from the middle one on the previous layer.

But Dr if we take T=5, then the central node in the time step 4 will be S(u^2d^2). Now from this node we can either go up or down.
If we go up we will get S(u^3d^2) and if we go down we will get S(u^2d^3).
What about the nodes like S(u^5), S(u^4d), s(ud^4) and s(d^5).
since we have T=5 (Time steps) so there will be 6 nodes, and from the central node in the previous layer we get only 2 nodes, what about the rest 4 nodes.

memonasif

Posts: 4
Joined: Fri Jun 24, 2011 8:38 pm

Re: Recombining trees

The way to approach multi-period binomial option pricing models is to figure out the stock and option prices in the latest period and work backward from there using any and all the formulas introduced in Sections 15 through 18.
Jacob555

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Joined: Thu Jan 31, 2013 7:20 am

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