otp.agg.option_price#
- option_price(volatility, interest_rate, compute_model, number_of_steps, compute_delta, compute_gamma, compute_theta, compute_vega, compute_rho, volatility_field_name, interest_rate_field_name, option_type_field_name, strike_price_field_name, days_in_year, days_till_expiration_field_name, expiration_date_field_name, running=False, bucket_interval=0, bucket_time='end', bucket_units=None, bucket_end_condition=None, boundary_tick_bucket='new')#
This aggregation requires several parameters to compute the option price. Those are, OPTION_TYPE, STRIKE_PRICE, EXPIRATION_DATE or DAYS_TILL_EXPIRATION, VOLATILITY, and INTEREST_RATE. Each parameter can be specified, either via a symbol parameter with the same name or via a tick field, by specifying the name of that field as an EP parameter, as follows. Besides, VOLATILITY and INTEREST_RATE can also be specified as parameters. If they are also specified as fields, the parameters value are ignored. In either case, the OPTION_TYPE value must be set to either CALL or PUT (case insensitive). EXPIRATION_DATE is in YYYYMMDD format, a string in case of a symbol parameter and an integer in case of a tick attribute. Additionally, NUMBER_OF_STEPS should be specified in case of Cox-Ross-Rubinstein method.
- Parameters
volatility (float) – The historical volatility of the asset’s returns.
interest_rate (float) – The risk-free interest rate.
compute_model (str) – Allowed values are BS and CRR. Choose between Black–Scholes (BS) and Cox-Ross-Rubinstein (CRR) models for computing call/put option price. Default: BS
number_of_steps (int) – Specifies the number of time steps between the valuation and expiration dates. This is a mandatory parameter for CRR model.
compute_delta (bool) – Specifies whether Delta is to be computed or not. This parameter is used only in case of BS model. Default: False
compute_gamma (bool) – Specifies whether Gamma is to be computed or not. This parameter is used only in case of BS model. Default: False
compute_theta (bool) – Specifies whether Theta is to be computed or not. This parameter is used only in case of BS model. Default: False
compute_vega (bool) – Specifies whether Vega is to be computed or not. This parameter is used only in case of BS model. Default: False
compute_rho (bool) – Specifies whether Rho is to be computed or not. This parameter is used only in case of BS model. Default: False
volatility_field_name (str) – Specifies name of the field, which carries the historical volatility of the asset’s returns. Default: empty
interest_rate_field_name (str) – Specifies name of the field, which carries the risk-free interest rate. Default: empty
option_type_field_name (str) – Specifies name of the field, which carries the option type (either CALL or PUT). Default: empty
strike_price_field_name (str) – Specifies name of the field, which carries the strike price of the option. Default: empty
days_in_year (int) – Specifies number of days in a year (say, 365 or 252 (business days, etc.). Used with DAYS_TILL_EXPIRATION parameter to compute the fractional years till expiration. Default: 365
days_till_expiration_field_name (str) – Specifies name of the field, which carries number of days till expiration of the option. Default: empty
expiration_date_field_name (str) – Specifies name of the field, which carries the expiration date of the option, in YYYYMMDD format. Default: empty
running (bool, default=False) –
Aggregation will be calculated as sliding window.
running
andbucket_interval
parameters determines when new buckets are created.running
= Trueaggregation will be calculated in a sliding window.
bucket_interval
= N (N > 0)Window size will be N. Output tick will be generated when tick “enter” window (arrival event) and when “exit” window (exit event)
bucket_interval
= 0Left boundary of window will be bound to start time. For each tick aggregation will be calculated in [start_time; tick_t].
running
= Falsebuckets partition the [query start time, query end time) interval into non-overlapping intervals of size
bucket_interval
(with the last interval possibly of a smaller size). Ifbucket_interval
is set to 0 a single bucket for the entire interval is created.Note that in non-running mode OneTick unconditionally divides the whole time interval into specified number of buckets. It means that you will always get this specified number of ticks in the result, even if you have less ticks in the input data.
Default: False
bucket_interval (int or Operation or OnetickParameter or
symbol parameter
, default=0) –Determines the length of each bucket (units depends on
bucket_units
).If
Operation
of bool type is passed, acts asbucket_end_condition
.Bucket interval can also be set with integer
OnetickParameter
orsymbol parameter
.bucket_time (Literal['start', 'end'], default=end) –
Control output timestamp.
start
the timestamp assigned to the bucket is the start time of the bucket.
end
the timestamp assigned to the bucket is the end time of the bucket.
bucket_units (Optional[Literal['seconds', 'ticks', 'days', 'months', 'flexible']], default=None) –
Set bucket interval units.
By default, if
bucket_units
andbucket_end_condition
not specified, set to seconds. Ifbucket_end_condition
specified, thenbucket_units
set to flexible.If set to flexible then
bucket_end_condition
must be set.Note that seconds bucket unit doesn’t take into account daylight-saving time of the timezone, so you may not get expected results when using, for example, 24 * 60 * 60 seconds as bucket interval. In such case use days bucket unit instead. See example in
onetick.py.agg.sum()
.bucket_end_condition (condition, default=None) –
An expression that is evaluated on every tick. If it evaluates to “True”, then a new bucket is created. This parameter is only used if
bucket_units
is set to “flexible”.Also can be set via
bucket_interval
parameter by passingOperation
object.boundary_tick_bucket (Literal['new', 'previous'], default=new) –
Controls boundary tick ownership.
previous
A tick on which
bucket_end_condition
evaluates to “true” belongs to the bucket being closed.new
tick belongs to the new bucket.
This parameter is only used if
bucket_units
is set to “flexible”
Note
This aggregation is used with
.apply()
, but latest OneTick builds support also the.agg()
method.Examples
Black–Scholes with parameters passed through symbol params and calculated delta:
>>> symbol = otp.Tick(SYMBOL_NAME='SYMB') >>> symbol['OPTION_TYPE'] = 'CALL' >>> symbol['STRIKE_PRICE'] = 100.0 >>> symbol['DAYS_TILL_EXPIRATION'] = 30 >>> symbol['VOLATILITY'] = 0.25 >>> symbol['INTEREST_RATE'] = 0.05 >>> data = otp.Ticks(PRICE=[100.7, 101.1, 99.5], symbol=symbol) >>> data = otp.agg.option_price(compute_delta=True).apply(data) >>> otp.run(data)['SYMB'] Time VALUE DELTA 0 2003-12-04 2.800999 0.50927 >>> data.schema {'VALUE': <class 'float'>, 'DELTA': <class 'float'>}
Cox-Ross-Rubinstein with parameters passed through fields:
>>> data = otp.Ticks( ... PRICE=[100.7, 101.1, 99.5], ... OPTION_TYPE=['CALL']*3, ... STRIKE_PRICE=[100.0]*3, ... DAYS_TILL_EXPIRATION=[30]*3, ... VOLATILITY=[0.25]*3, ... INTEREST_RATE=[0.05]*3, ... ) >>> data = otp.agg.option_price( ... compute_model='CRR', ... number_of_steps=5, ... option_type_field_name='OPTION_TYPE', ... strike_price_field_name='STRIKE_PRICE', ... days_till_expiration_field_name='DAYS_TILL_EXPIRATION', ... volatility_field_name='VOLATILITY', ... interest_rate_field_name='INTEREST_RATE', ... ).apply(data) >>> otp.run(data) Time VALUE 0 2003-12-04 2.937537
Black–Scholes with some parameters passed through parameters:
>>> data = otp.Ticks( ... PRICE=[100.7, 101.1, 99.5], ... OPTION_TYPE=['CALL']*3, ... STRIKE_PRICE=[100.0]*3, ... DAYS_TILL_EXPIRATION=[30]*3, ... ) >>> data = otp.agg.option_price( ... option_type_field_name='OPTION_TYPE', ... strike_price_field_name='STRIKE_PRICE', ... days_till_expiration_field_name='DAYS_TILL_EXPIRATION', ... volatility=0.25, ... interest_rate=0.05, ... ).apply(data) >>> otp.run(data) Time VALUE 0 2003-12-04 2.800999
To compute values for each tick in a series, set
bucket_interval=1
andbucket_units='ticks'
>>> data = otp.Ticks( ... PRICE=[110.0, 101.0, 112.0], ... OPTION_TYPE=["CALL"]*3, ... STRIKE_PRICE=[110.0]*3, ... DAYS_TILL_EXPIRATION=[30]*3, ... VOLATILITY=[0.2]*3, ... INTEREST_RATE=[0.05]*3 ... ) >>> data = otp.agg.option_price( ... option_type_field_name='OPTION_TYPE', ... strike_price_field_name='STRIKE_PRICE', ... days_till_expiration_field_name='DAYS_TILL_EXPIRATION', ... volatility_field_name='VOLATILITY', ... interest_rate_field_name='INTEREST_RATE', ... bucket_interval=1, ... bucket_units='ticks', ... ).apply(data) >>> otp.run(data) Time VALUE 0 2003-12-01 00:00:00.000 2.742714 1 2003-12-01 00:00:00.001 0.212927 2 2003-12-01 00:00:00.002 3.945447
Usage with the
.agg()
method (on the latest OneTick builds).data = otp.Ticks( PRICE=[100.7, 101.1, 99.5], OPTION_TYPE=['CALL']*3, STRIKE_PRICE=[100.0]*3, DAYS_TILL_EXPIRATION=[30]*3, ) data = data.agg({ 'RESULT': otp.agg.option_price( option_type_field_name='OPTION_TYPE', strike_price_field_name='STRIKE_PRICE', days_till_expiration_field_name='DAYS_TILL_EXPIRATION', volatility=0.25, interest_rate=0.05, ) }) df = otp.run(data) print(df)
Time RESULT 0 2003-12-04 2.800999
The following examples show results for different cases of option price calculation. Results are compared with two online calculators: Drexel University (DU) and Wolfram Alpha (WA).
Call option, strike price 110.0, underlying price 120.0, volatility 20.0%, interest 5.0%, expiring in 15 days.
>>> data = { ... "PRICE": 120., ... "OPTION_TYPE": "call", ... "STRIKE_PRICE": 110., ... "DAYS_TILL_EXPIRATION": 15, ... "VOLATILITY": 0.2, ... "INTEREST_RATE": 0.05, ... } >>> data = otp.Tick(**data) >>> data = otp.agg.option_price( ... option_type_field_name='OPTION_TYPE', ... strike_price_field_name='STRIKE_PRICE', ... days_till_expiration_field_name='DAYS_TILL_EXPIRATION', ... volatility_field_name='VOLATILITY', ... interest_rate_field_name='INTEREST_RATE', ... compute_delta=True, ... compute_gamma=True, ... compute_theta=True, ... compute_vega=True, ... compute_rho=True ... ).apply(data) >>> res = otp.run(data).drop("Time", axis=1) >>> for key, val in res.to_dict(orient='list').items(): ... print(f"{key}={val[0]}") VALUE=10.248742578738629 DELTA=0.9866897658932824 GAMMA=0.007022082258701294 THETA=-7.430061156928735 VEGA=0.8311067221257422 RHO=4.444686136785831
# Field
OneTick
DU benchmark
WA benchmark
VALUE
10.248742578738629
10.248742577611323400
10.249
DELTA
0.9866897658932824
0.986689766547165200
0.987
GAMMA
0.007022082258701294
0.007022082258701300
0.007
THETA
-7.430061156928735
-7.430061160908399600
-7.430
VEGA
0.8311067221257422
0.831106722125743000
0.831
RHO
4.444686136785831
4.444686140056785400
4.445
Put option, strike price 110.0, underlying price 120.0, volatility 20.0%, interest 5.0%, expiring in 15 days.
data = { "PRICE": 120., "OPTION_TYPE": "put", "STRIKE_PRICE": 110., "DAYS_TILL_EXPIRATION": 15, "VOLATILITY": 0.2, "INTEREST_RATE": 0.05, } data = otp.Tick(**data) data = otp.agg.option_price( option_type_field_name='OPTION_TYPE', strike_price_field_name='STRIKE_PRICE', days_till_expiration_field_name='DAYS_TILL_EXPIRATION', volatility_field_name='VOLATILITY', interest_rate_field_name='INTEREST_RATE', compute_delta=True, compute_gamma=True, compute_theta=True, compute_vega=True, compute_rho=True ).apply(data) res = otp.run(data).drop("Time", axis=1) for key, val in res.to_dict(orient='list').items(): print(f"{key}={val[0]:.14f}")
VALUE=0.02294724243400 DELTA=-0.01331023410672 GAMMA=0.00702208225870 THETA=-1.94135092374397 VEGA=0.83110672212574 RHO=-0.06658254802357
# Field
OneTick
DU benchmark
WA benchmark
VALUE
0.022947242433995818
0.022947241306682900
0.023
DELTA
-0.013310234106717611
-0.013310233452834800
-0.013
GAMMA
0.007022082258701294
0.007022082258701300
0.007
THETA
-1.94135092374397
-1.941350927723632000
-1.941
VEGA
0.8311067221257422
0.831106722125743000
0.831
RHO
-0.06658254802356636
-0.066582544752611000
-0.067
Put option, strike price 90.0, underlying price 80.0, volatility 30.0%, interest 8.0%, expiring in 20 days.
data = { "PRICE": 80., "OPTION_TYPE": "put", "STRIKE_PRICE": 90., "DAYS_TILL_EXPIRATION": 20, "VOLATILITY": 0.3, "INTEREST_RATE": 0.08, } data = otp.Tick(**data) data = otp.agg.option_price( option_type_field_name='OPTION_TYPE', strike_price_field_name='STRIKE_PRICE', days_till_expiration_field_name='DAYS_TILL_EXPIRATION', volatility_field_name='VOLATILITY', interest_rate_field_name='INTEREST_RATE', compute_delta=True, compute_gamma=True, compute_theta=True, compute_vega=True, compute_rho=True ).apply(data) res = otp.run(data).drop("Time", axis=1) for key, val in res.to_dict(orient='list').items(): print(f"{key}={val[0]}")
VALUE=9.739720671039635 DELTA=-0.9429118423759162 GAMMA=0.020391626464263516 THETA=0.9410250231811439 VEGA=2.1453108389800515 RHO=-4.666995510197969
# Field
OneTick
DU benchmark
WA benchmark
VALUE
9.739720671039635
9.739720664487278600
9.740
DELTA
-0.9429118423759162
-0.942911845180447200
-0.943
GAMMA
0.020391626464263516
0.020391626464263600
0.020
THETA
0.9410250231811439
0.941025040605956600
0.941
VEGA
2.1453108389800515
2.145310838980050700
2.145
RHO
-4.666995510197969
-4.666995522132770800
-4.667
Call option, strike price 90.0, underlying price 80.0, volatility 30.0%, interest 8.0%, expiring in 20 days.
>>> data = { ... "PRICE": 80., ... "OPTION_TYPE": "call", ... "STRIKE_PRICE": 90., ... "DAYS_TILL_EXPIRATION": 20, ... "VOLATILITY": 0.3, ... "INTEREST_RATE": 0.08, ... } >>> data = otp.Tick(**data) >>> data = otp.agg.option_price( ... option_type_field_name='OPTION_TYPE', ... strike_price_field_name='STRIKE_PRICE', ... days_till_expiration_field_name='DAYS_TILL_EXPIRATION', ... volatility_field_name='VOLATILITY', ... interest_rate_field_name='INTEREST_RATE', ... compute_delta=True, ... compute_gamma=True, ... compute_theta=True, ... compute_vega=True, ... compute_rho=True ... ).apply(data) >>> res = otp.run(data).drop("Time", axis=1) >>> for key, val in res.to_dict(orient='list').items(): ... print(f"{key}={val[0]:.13f}") VALUE=0.1333777785229 DELTA=0.0570881576241 GAMMA=0.0203916264643 THETA=-6.2274824082202 VEGA=2.1453108389801 RHO=0.2429410866523
# Field
OneTick
DU benchmark
WA benchmark
VALUE
0.13337777852292199
0.133377771970562400
0.133
DELTA
0.05708815762408384
0.057088154819552600
0.057
GAMMA
0.020391626464263516
0.020391626464263600
0.020
THETA
-6.227482408220195
-6.227482390795381800
-6.227
VEGA
2.1453108389800515
2.145310838980050700
2.145
RHO
0.2429410866522622
0.242941074717460500
0.243
Call option, strike price 140.0, underlying price 150.0, volatility 60.0%, interest 7.0%, expiring in 10 days.
>>> data = { ... "PRICE": 150., ... "OPTION_TYPE": "call", ... "STRIKE_PRICE": 140., ... "DAYS_TILL_EXPIRATION": 10, ... "VOLATILITY": 0.6, ... "INTEREST_RATE": 0.07, ... } >>> data = otp.Tick(**data) >>> data = otp.agg.option_price( ... option_type_field_name='OPTION_TYPE', ... strike_price_field_name='STRIKE_PRICE', ... days_till_expiration_field_name='DAYS_TILL_EXPIRATION', ... volatility_field_name='VOLATILITY', ... interest_rate_field_name='INTEREST_RATE', ... compute_delta=True, ... compute_gamma=True, ... compute_theta=True, ... compute_vega=True, ... compute_rho=True ... ).apply(data) >>> res = otp.run(data).drop("Time", axis=1) >>> for key, val in res.to_dict(orient='list').items(): ... print(f"{key}={val[0]:.13f}") VALUE=12.2728332229748 DELTA=0.7774682547236 GAMMA=0.0200066930955 THETA=-88.3314253858302 VEGA=7.3997358024512 RHO=2.8588330133030
# Field
OneTick
DU benchmark
WA benchmark
VALUE
12.272833222974782
12.272833124496244700
12.27
DELTA
0.7774682547235652
0.777468265655730700
0.777
GAMMA
0.020006693095516285
0.020006693095516300
0.020
THETA
-88.33142538583016
-88.331425507511386000
-88.331
VEGA
7.399735802451228
7.399735802451227600
7.400
RHO
2.858833013303013
2.858833060927763500
2.859
Put option, strike price 140.0, underlying price 150.0, volatility 60.0%, interest 7.0%, expiring in 10 days.
data = { "PRICE": 150., "OPTION_TYPE": "put", "STRIKE_PRICE": 140., "DAYS_TILL_EXPIRATION": 10, "VOLATILITY": 0.6, "INTEREST_RATE": 0.07, } data = otp.Tick(**data) data = otp.agg.option_price( option_type_field_name='OPTION_TYPE', strike_price_field_name='STRIKE_PRICE', days_till_expiration_field_name='DAYS_TILL_EXPIRATION', volatility_field_name='VOLATILITY', interest_rate_field_name='INTEREST_RATE', compute_delta=True, compute_gamma=True, compute_theta=True, compute_vega=True, compute_rho=True).apply(data) res = otp.run(data).drop("Time", axis=1) for key, val in res.to_dict(orient='list').items(): print(f"{key}={val[0]:.13f}")
VALUE=2.0045973669685 DELTA=-0.2225317452764 GAMMA=0.0200066930955 THETA=-78.5502018957506 VEGA=7.3997358024512 RHO=-0.9694344974913
# Field
OneTick
DU benchmark
WA benchmark
VALUE
2.0045973669685395
2.004597268490016500
2.00
DELTA
-0.22253174527643482
-0.222531734344269000
-0.223
GAMMA
0.020006693095516285
0.020006693095516300
0.020
THETA
-78.5502018957506
-78.550202017431814100
-78.550
VEGA
7.399735802451228
7.399735802451227600
7.400
RHO
-0.9694344974913363
-0.969434449866586000
-0.969
See also
OPTION_PRICE OneTick event processor