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mbacke
Topic Author
Posts: 11
Joined: May 18th, 2003, 2:29 pm

### dual methods for american options

does anybody know a webpage where i can get a matlab implementation of Haugh and kogan dual pricing of american option?

Forde
Posts: 124
Joined: November 27th, 2002, 7:45 pm

### dual methods for american options

unfortunately no, altho could u explain what u mean by dual pricing, and which papers you're referring to - are you talking about an equivalent formulation of the American pricing problem where S and K are switched round, and time is run backwards?

mbacke
Topic Author
Posts: 11
Joined: May 18th, 2003, 2:29 pm

### dual methods for american options

I am referring to the paper of Haugh and Kogan entitlted 'Pricing american option: A duality approach'.Basically, they are using a technique which allows them to get an upper bound for the price of the american option.

mbacke
Topic Author
Posts: 11
Joined: May 18th, 2003, 2:29 pm

### dual methods for american options

i have found a web related to this. they are using java, a language i don't understand. the webpage is martingale.berlios.deis there anybody who could tell what they are doing?

brunette
Posts: 1
Joined: September 17th, 2003, 5:57 pm

### dual methods for american options

I currently work about bermudan swaption pricing so i will be interest if someone have an implementation of Andersen approach ! thanks a lot !

Steno
Posts: 96
Joined: December 6th, 2001, 11:29 am

### dual methods for american options

The terms 'dual' and 'duality' are used in many contexts with different meanings. In this case, I believe 'duality' is to be understood in the context of optimization. Pricing of American or Bermudan options can be restated as an optimal stopping problem, i.e. finding an exercise strategy that maximizes the value of the option (as a function of the exercise strategy). A dual problem to his maximization problem is a minimization problem on a dual space, defined by the same data, and with the property that the objective function of the maximization problem (primal problem) is less than or equal to the objective function of the dual problem (s.t. the same holds for the respective optima). Now, the interesting dual problems are of course those for which the supremum of the primal problem equals the infimum of the dual problem, and even more so for problems where these optima are attained. This can be done for linear and convex optimization problems - the most prominent example being linear programming in euclidean spaces - but the theory can be extended to infinite-dimensional linear vector spaces (viz. Luenbergers book 'Optimization by vector space methods'), but the concept of duality can be extended to non-convex optimization as well by the concept of dual functions (as opposed to dual multipliers). Indeed, one can define a hierarchy of dual problems, by restricting the subset defining the set of feasible solutions of the dual problem. This gives a tradeoff between selecting a dual problem that is computationally tractable versus one that gives tight bounds at higher computational costs

trc
Posts: 95
Joined: April 4th, 2002, 2:28 pm

### dual methods for american options

mbacke,For the Haugh-Kogan approach (Theorem 4.6.2, p106 in the book on my website) you have to estimate the constant K and that will involve the computation of many conditional expectations E_t(U_{t+1}-U_t) along a large number of paths over which you have to average. It's a massive computation. This why I have not implemented it. So you are not missing anything.The approach of Rogers (p 107) has similar problems. You have to guess a suitable supermartingale to get an upper estimate. The only supermartingale guarenteed to work well is the price process itself or something close to it (a hedging strategy).MJ was able to make this work in the case of Bermudan swaptions in a Libor market model, where the computational burden is particularlypainful. In his paper he is not very explicit about the supermartingale used in the estimate. Maybe he can tell us how long this computation took and how close he believes his supermartingale was to the actual price process.
Last edited by trc on September 24th, 2003, 10:00 pm, edited 1 time in total.

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