March 31st, 2004, 11:33 am
Up to discounting it is the same (which is missing as "mib" pointed out in the other thread).The only thing might be numerical problems with high order Laguerre: one comes throughthe oscillating integral (see below) and the other through significant digits and roots forthe Laguerre polynomial: for order 64 the 'last' root is around 250 (i do not know it for a degree of 150) where it islikely that you get rounding errors _even if you have the exact root_ (which itself may bea problem). Otherwise stated: high order does not mean high exactness, it might result inthe converse. As i have only 15 digits in Excel i dicided to take a lower order.For highly oscillating integrands your nodes may be placed not that well w r t periodics,and for the following input the DLL gives a price of 29,9999999832 - below 30:Stock 100Strike 70Current Variance 0,04Long term Variance 0,04Mean reversion speed 1,15Volvol 0,39Interest Rate 0Time to expiry 0,03Correlation -0,64Market Price of Vol Risk 0Practical that is not a deep problem, but i think you will have exacter results takinglower order (which can adopt to the periodics) and do repeated finite integrationsand if you like Gauss Laguerre do one at the end.