I embed Maple code in Mobius for test questions. A simple 2-step CRR tree gives significantly different answer from the calculated by hand or by R's fOptions. Here is the piece of Mobius/Maple:

$ct = maple("

with(Finance):

S0:=50; X:=50; Ty:=6./12; r:=0.07; sig:=0.3156; n:=1;

dt := Ty/n;

u := exp(sig*sqrt(dt));

d := 1/u;

pu := (exp(r*dt) - d)/(u - d);

pd := 1 - pu;

BT := BinomialTree(Ty,n,S0,u,pu,d,pd);

cT := ST -> max(ST - $X,0);

Ec := EuropeanOption(cT, $Ty):

LatticePrice(Ec,BT,$r);

");

The answer is: 6.545478168. Exactly the same with BlackScholesBinomialTree

The correct answer should be 6.32

In this case the solution by hand is simply e^(-0.07*05)*0.5236*$12.50

R confirms 6.32:

CRRBinomialTreeOption(TypeFlag = "ce", S=S, X=X, Time=T, r=r, b=b, sigma=sig, n=n)@price

The error decreases with the increase of number of steps. All quantities before LatticePrice are calculated corectly. Any idea of what the reason might be?

Thanks.

Dear,

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