scripted payoff for Monte Carlo

[P Nelnik]

Good morning all,

I think that it would be really useful to be able to define a payoff using a script.
But it seems that such a solution does not yet exist.

The aim would be to allow users specify a payoff in a script which would not require the C++ project to be recompiled.
The payoff script could be used in the MC engine.

Here are some suggestions,
___________________________________________________________________
Development phase 1 could enable the following for use in a MC engine:

(i) at run-time, the user would pass in
             1: an array which contained the constants required to specify the payoff,
      and  2: the payoff script
      for a vanilla call, the input array would be of length 1 and it would contain the strike.
      the payoff script would just be:       value = DiscFact[numTimeSteps - 1] * max( 0, Spot[numTimeSteps - 1] - input_array[0] );  
     
(ii) after some initial pre-processing, the evaluation script would be called once for each simulation

(iii) there are 3 predefined variables:
      numTimeSteps    the number of time steps in the path
      Spot[0, ... , numTimeSteps-1]  array of spot prices for one given path
      DiscFact[0, ... , numTimeSteps-1] array of discount factors
      
(iv) the payoff scripting language would need:
         for loop,
         if statement
         the assignment operator
         some basic comparison operators ==, >=, <=, <, >
         some simple maths operators: +,-,*./,^,
         some simple functions, exp(.), log(..), min(.,,), max(.,.)
         the only types would be double (real) and array of doubles
___________________________________________________________________
  
It would be nice if it were set-up in such a way that it worked well with a range of different underlying types: equity, fx, interest-rate, commodity, credit.


Possible extentions:
A: enable it to be called from (my favourite) excel
B: allow the user to give names to the input variables, for example strike, this will make scripts much more legible
C: allow functions to be defined in the scripts
D: for efficiency there would be numerous vector based functions available which would be much faster than for-loops
E: allow multi factor underlyings, so the spot above would become a matrix  S[ num_underlyings, num_time_steps]

If we're a little bit clever in designing the code, then they would be much code re-use when extending it to be used in the PDE solver,
though in that case, clearly the user wouldn't have access to a full (simulation) path spot[0,..,numTimeSteps-1]

Regards
Philip

P.S. there is an old discussion which touches on this: http://old.nabble.com/Question-regarding-range-of-strings-in-ObjectHandler-td18009446.html


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