February 2nd, 2008, 11:37 am
Extreme case of 1000 * 1000 grid ( Call = 61.30295, Put = 7.17124) Actual values should be closer to 61.09639 and 6.94701 (computed using another finite difference off-the shelf algorithm that i believe to be reliable)S = 100, K = 50, vol = 70%, r = 5%, q = 0, T= 1.81I priced a Put (call is easy) using exponential fitting, 1/2-implicit penalty method with eps = 0.001 and CN time averaging using:NS = 500, NT >= 2.5 * 1000 at S = 100Then P = 6.948225with a variety of Smax (6*K, 10*K, 20*K). Agrees with your 'reliable' FDM. BTW, is it a commercial package or your own FDM? So, problems even with no dividend. Since you have not said which scheme you use exactly, I can only guess why your price is wrong. Normally, small vol is a problem but not large vol (BTW fitting works with any vol!). A wild guess is your centred differencing starts hicking for large vol??Maybe try a vol = .2 and see what answer you get. //The greeks for above are del = -0.1009, gamma = 0.001958, theta = -3.8355I also check ITM prices for S20==> 30.6498530, 24.0903540, 19.38250, 15.8698370, 11.0754980, 9.40189190, 8.051373 Quote S does not fall on a grid point and i order to get the Option premium at underlying i use a cubic interpolation methodPut it on a grid point and see what happens
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Cuchulainn on February 1st, 2008, 11:00 pm, edited 1 time in total.