Securities and Options 73
Example 1: An option has 6 months to run and a strike price of $45. Find Call and Put
values assuming a spot price of $52, return volatility of 20.54% per month and a risk-free
interest rate of ½% per month. Show how to re-scale n, i and PMT to use a yearly time
unit, and how to re-scale them back again to the original monthly basis.
12c platinum / 12C
RPN Keystrokes
12c platinum
ALG Keystrokes
Display Comments
6n 6n
6.00
Time to expiry (months).
.5¼ .5¼
0.50
Interest rate (% per month).
52$ 52$
52.00
Stock price.
20.54P 20.54P
20.54
Volatility (% per month).
45M 45M
45.00
Strike price.
t t
14.22
Call value.
~ ~
5.89
Put value.
:gAn :gAn
0.50
Years to expiry.
:gC¼ :gC¼
6.00
Yearly interest rate %.
:P
12gr§P
:P§
12grP
71.15
Yearly volatility %.
t t
14.22
Call value (unchanged).
:ngA :ngA
6.00
Months to expiry.
:¼gC :¼gC
0.50
Monthly interest rate %.
:P
12grzP
:Pz
12grP
20.54
Monthly volatility %.
The next example is Example 12.7 from Options, Futures, and Other Derivatives (5th
Edition) by John C. Hull (Prentice Hall, 2002).
Example 2: The stock price six months from the expiration of an option is $42, the
exercise price of the option is $40, the risk-free interest rate is 10% per annum, and the
volatility is 20% per annum. Find Call and Put values.
12c platinum / 12C
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12c platinum
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Display Comments
.5n .5n
0.50
Time to expiry (years).
10¼ 10¼
10.00
Interest rate (% per year).
42$ 42$
42.00
Stock price.
20P 20P
20.00
Volatility (% per year).
40M 40M
40.00
Strike price.
t t
4.76
Call value.
~ ~
0.81
Put value.