The Black–Scholes formulas for the prices of European calls and puts on a non-dividend paying stock are:
C = SN(d1) – Xe-rT N(d2)
P = Xe-rT N(-d2)- SN(-d1)
Where d1 = [ ln s/x +(r+δ2/2)T ]/ δ √T
And d2 = d1 –δ√T
• The Black Scholes equation is done in continuous time. This requires...