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) –
See Aggregation buckets guide to see examples of how this parameter works.

Specifies if the aggregation will be calculated as a sliding window. running and bucket_interval parameters determines when new buckets are created.
- running = True
  
  aggregation 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 = 0
    
    Left boundary of window will be set to query start time. For each tick aggregation will be calculated in the interval [start_time; tick_t] from query start time to the tick’s timestamp (inclusive).
- running = False (default)
  
  buckets 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). If bucket_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 float or Operation or OnetickParameter or symbol parameter or datetime offset object, default=0) –
Determines the length of each bucket (units depends on bucket_units).

If Operation of bool type is passed, acts as bucket_end_condition.

Bucket interval can also be set as a float value if bucket_units is set to seconds. Note that values less than 0.001 (1 millisecond) are not supported.

Bucket interval can be set via some of the datetime offset objects: otp.Milli, otp.Second, otp.Minute, otp.Hour, otp.Day, otp.Month. In this case you could omit setting bucket_units parameter.

Bucket interval can also be set with integer OnetickParameter or symbol 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 and bucket_end_condition not specified, set to seconds. If bucket_end_condition specified, then bucket_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 passing Operation 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 and bucket_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

Table 1 Benchmark comparison#
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

Table 2 Benchmark comparison#
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

Table 3 Benchmark comparison#
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

Table 4 Benchmark comparison#
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

Table 5 Benchmark comparison#
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

Table 6 Benchmark comparison#
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