Black-Scholes Formula for Valuing European Options. HP 12C Platinum Financial Calculator, 12c

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

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 % / 1 0 0 )

, 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.

DPN j

RDV j j = period number.

= depreciation expense during period j.

RBV

Y

1 j

= remaining depreciable value at end of period j

= RDV

j–1

– DPN j

where RDV

0

= SBV – SAL

= remaining book value = RBV

j–1

– DPN j

where RBV

0

= SBV

= number of months in partial first year.

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