April 27th, 2012, 4:12 pm
They state that using alpha=1/2 and the BS control variate with vol taken at 0 is the best thing to do for rewards with no sweat.Then there is a 5pp. section 8.4.4 "Refinements of Numerical Implementation" making heavy references to this paper by Bang.The idea there seems to apply whether or not you use the BS control variate, it's about computing the right tail of the integral (no mapping of [0 inf) to [0 1] here) as the sum of two terms, the main one given as E_{1} exponential integral functions.Me, I just want a method using CF and/or saddlepoint that will compute call prices to 4 places relative accuracy for all logmoneyness in [-2.3, 2.3] and "all" param combos.