[Quantlib-dev] Greeks for vanilla binomial - implementation

[steve.affine <st...@af...>]

Concerning the FR to add Greeks
(http://sourceforge.net/tracker/index.php?func=detail&aid=910972&group_id=12740&atid=362740),
I have looked at this today and implemented most of them.

My suggestion is to use points on the binomial tree as per Odergaard
(http://finance-old.bi.no/~bernt/gcc_prog/recipes/recipes.pdf).

This gives delta, gamma & theta in quick and straightforward way without the
need for recomputation. The code in binomialengine.hpp is basically:

        DiscretizedVanillaOption option(arguments_);

		//Go to maturity
        option.initialize(lattice, maturity);

		//Partial derivatives calculated from various points in the binomial tree
(Odegaard)

		//Rollback to third-last step, and get underlying price (s) & option value
(p) at this point
		option.rollback(grid[2]);
		Array va2(option.values());
		QL_ASSERT(va2.size() == 3, "Expect 3 nodes in grid at second step");
		Real p2h = va2[2]; // high-price
		Real p2m = va2[1]; // mid-price
		Real s2 = bslattice->underlying(2, 2); //high price

		//Rollback to second-last step, and get underlying price (s) & option
value (p) at this point
		option.rollback(grid[1]);
		Array va(option.values());
		QL_ASSERT(va.size() == 2, "Expect 2 nodes in grid at first step");
		Real p1 = va[1];

		//Rollback to t=0
        option.rollback(0.0);
		Real p0 = option.presentValue();
		Real s1 = bslattice->underlying(1, 1);

		//Calc partials
		Real delta0 = (p1-p0)/(s1-s0);	//dp/ds
		Real delta1 = (p2h-p1)/(s2-s1);	//dp/ds

		//Return results
		results_.value = p0;
		results_.delta = delta0;
		results_.gamma = 2.0*(delta1-delta0)/(s2-s0);			//d(delta)/ds
		results_.theta = (p2m-p0)/(grid[2]);					//dp/dT

Any comments on this? Does anyone disagree, or think there is a better
method or better place to put this code?

cheers
Steve

affine group limited
http://www.affine.hk 
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