Appendix B. BSM Option Class
Class Definition
The following presents a class definition for a European call option in the Black-Scholes-Merton (1973) model. The class-based implementation is an alternative to the one based on functions as presented in “Python Script”:
#
# Valuation of European call options in Black-Scholes-Merton model
# incl. vega function and implied volatility estimation
# -- class-based implementation
#
# Python for Finance, 2nd ed.
# (c) Dr. Yves J. Hilpisch
#
from
math
import
log
,
sqrt
,
exp
from
scipy
import
stats
class
bsm_call_option
(
object
):
''' Class for European call options in BSM model.
Attributes
==========
S0: float
initial stock/index level
K: float
strike price
T: float
maturity (in year fractions)
r: float
constant risk-free short rate
sigma: float
volatility factor in diffusion term
Methods
=======
value: float
returns the present value of call option
vega: float
returns the vega of call option
imp_vol: float
returns the implied volatility given option quote
'''
def
__init__
(
self
,
S0
,
K
,
T
,
r
,
sigma
):
self
.
S0
=
float
(
S0
)
self
.
K
=
K
self
.
T
=
T
self
.
r
=
r
self
.
sigma
=
sigma
def
value
(
self
):
''' Returns option value.
'''
d1
=
((
log
(
self
.
S0
/
self
.
K
)
+
(
self
.
r
+
0.5
*
self
.
sigma
**
2
)
*
self
.
T
)
/
(
self
.
sigma
*
sqrt
(
self
.
T
)))
d2
=
((
log
(
self
.
S0
/
self
.
K
)
+
(
self
.
r
-
0.5
*
self
.
sigma
**
2
)
*
self
.
T
)
/
(
self
.
sigma
*
sqrt
(
self
.
T
)))
value
=
(
self
.
S0
*
stats
.
norm
.
cdf
(
d1
,
0.0
,
1.0
)
-
self
.
K
*
exp
(
-
self
.
r
*
self
.
T
)
*
stats
.
norm
.
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