HP 12C - Black-Scholes Formula for Valuing European Options; Depreciation

254 Appendix E: Formulas Used
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 254 of 275
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm
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
1
) – Q × N(d
2
)
Put Value = Call Value + Q – P
where :
d
1
= LN(P/Q)/v + v/2, d
2
-= d
1
– v
Q
= Xe
(–T × r %/100)
, v=s%/100×
T
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
j
= depreciation expense during period j.
RDV
j
= remaining depreciable value at end of period j
= RDV
j–1
– DPN
j
where RDV
0
= SBV – SAL
RBV
j
= remaining book value = RBV
j–1
– DPN
j
where RBV
0
= SBV
Y
1
= number of months in partial first year.