Black-Scholes Formula For Valuing European Options; Depreciation - HP 12C User Manual

254 Appendix E: Formulas Used

Black-Scholes Formula for Valuing European Options

P = current asset price.
r% = risk-free rate (continuous, per time unit).
s% = volatility (continuous, per time unit).
T = term of option (same time unit as r% and s%).
X = exercise price of option.
N(z) = probability that a unit normal random variable is less than z.
Call Value = P × N(d
Put Value = Call Value + Q – P
where :
d = LN(P/Q)/v + v/2, d
1
Q = Xe

Depreciation

L = asset's useful life expectancy.
SBV = starting book value.
SAL = salvage value.
FACT = declining-balance factor expressed as a percentage.
j = period number.
DPN = depreciation expense during period j.
j
RDV = remaining depreciable value at end of period j
j
= RDV
RBV = remaining book value = RBV
j
Y = number of months in partial first year.
1
File name: hp 12c pt_user's guide_English_HDPMF123E27
Printed Date: 2005/8/1
) – Q × N(d )
1 2
-= d – v
2 1
( – T × r % / 1 0 0 )
, v=s%/100× T
– DPN where RDV = SBV – SAL
j–1 j 0
– DPN
j–1
Page: 254 of 275
Dimension: 14.8 cm x 21 cm
where RBV = SBV
j 0