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

Appendix E: Formulas Used 259
File name: HP 12c Pt Converted_user's guide_English_HDP0F123E02_080207 Page: 257 of 281
Printed Date: { 2007/8/2Dimension: 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.