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This release includes the Binomial Model, a mathematical model for pricing both American as well as European options. The Binomial Model is a discrete-time model that calculates the price of an option by creating a riskless hedge portfolio that replicates the payoff of the option. The model is based on the assumption that the price of the underlying asset follows a binomial distribution. The Binomial Model is a simple and intuitive model that is widely used in practice. It is also the basis for more complex models. See for an elaborate explanation the documentation as found here.
It returns a large DataFrame with the binomial tree for each company and each strike price around the current price (as defined by the start_date parameter).
The resulting output is a DataFrame containing the tickers, strike prices and movements as the index and the time to expiration as the columns. The movements index contains the number of up movements and the number of down movements. The output is the binomial tree displayed in a table. E.g. when using 10 time steps, the table for each strike price from each company will contain the actual binomial tree as also depicted in the image as seen below. Find the documentation here.
When selecting for example Apple at a Strike Price of 140 you will get the actual Binomial Tree depicted as a table, this represents the tree you see in the image at the top.
Movement
2024-02-02
2024-03-09
2024-04-15
2024-05-21
2024-06-27
2024-08-02
2024-09-08
2024-10-14
2024-11-20
2024-12-26
2025-02-01
UUUUUUUUUU
54.7747
69.9327
87.4757
107.31
129.344
153.573
180.122
209.208
241.069
275.965
314.18
UUUUUUUUUD
nan
39.9569
52.8423
68.2288
86.0206
106.037
128.14
152.365
178.911
207.994
239.852
UUUUUUUUDD
nan
nan
27.3011
37.7763
50.8718
66.5774
84.6651
104.825
126.925
151.146
177.689
UUUUUUUDDD
nan
nan
nan
16.9659
24.8886
35.4656
48.9066
65.0645
83.4462
103.602
125.698
UUUUUUDDDD
nan
nan
nan
nan
9.1158
14.4288
22.208
33.0259
47.083
63.8384
82.2161
UUUUUDDDDD
nan
nan
nan
nan
nan
3.8311
6.7007
11.4806
19.124
30.5822
45.85
UUUUDDDDDD
nan
nan
nan
nan
nan
nan
0.9669
1.9327
3.8631
7.722
15.4353
UUUDDDDDDD
nan
nan
nan
nan
nan
nan
nan
0
0
0
0
UUDDDDDDDD
nan
nan
nan
nan
nan
nan
nan
nan
0
0
0
UDDDDDDDDD
nan
nan
nan
nan
nan
nan
nan
nan
nan
0
0
DDDDDDDDDD
nan
nan
nan
nan
nan
nan
nan
nan
nan
nan
0
The model contains parameters to lengthen the time steps, change the risk-free rate and the dividend yield but more importantly, make it possible to calculate the price of both American and European options as well as Call and Put options. For example, let's calculate the price of a American Put option with a strike price of 140 for Apple again:
Which returns the Option valuations for an American Put Option.
Movement
2024-02-02
2024-03-03
2024-04-02
2024-05-03
2024-06-02
2024-07-03
2024-08-02
2024-09-01
2024-10-02
2024-11-01
2024-12-02
2025-01-01
2025-02-01
UUUUUUUUUUUU
2.3581
1.1115
0.4236
0.116
0.0171
0
0
0
0
0
0
0
0
UUUUUUUUUUUD
nan
3.7011
1.8524
0.7546
0.2225
0.0355
0
0
0
0
0
0
0
UUUUUUUUUUDD
nan
nan
5.6933
3.0346
1.3274
0.4238
0.0736
0
0
0
0
0
0
UUUUUUUUUDDD
nan
nan
nan
8.5588
4.8737
2.3002
0.8005
0.1529
0
0
0
0
0
UUUUUUUUDDDD
nan
nan
nan
nan
12.5322
7.6463
3.9148
1.4975
0.3173
0
0
0
0
UUUUUUUDDDDD
nan
nan
nan
nan
nan
17.8023
11.6676
6.518
2.7676
0.6586
0
0
0
UUUUUUDDDDDD
nan
nan
nan
nan
nan
nan
24.4233
17.2193
10.5575
5.0375
1.3671
0
0
UUUUUDDDDDDD
nan
nan
nan
nan
nan
nan
nan
32.2051
24.4052
16.5049
8.9884
2.8376
0
UUUUDDDDDDDD
nan
nan
nan
nan
nan
nan
nan
nan
40.6414
32.9347
24.6074
15.6102
5.89
UUUDDDDDDDDD
nan
nan
nan
nan
nan
nan
nan
nan
nan
48.9936
41.9389
34.3151
26.0772
UUDDDDDDDDDD
nan
nan
nan
nan
nan
nan
nan
nan
nan
nan
56.6615
50.2044
43.2257
UDDDDDDDDDDD
nan
nan
nan
nan
nan
nan
nan
nan
nan
nan
nan
63.702
57.7929
DDDDDDDDDDDD
nan
nan
nan
nan
nan
nan
nan
nan
nan
nan
nan
nan
70.1673
Under the hood of this model the stock prices are simulated based on up and down movements. These can be graphically depicted as a binomial tree and help in understanding the calculated option prices for each node in. More information about these stock price simulations can be found in the documentation here and as follows:
Which would return for Apple the following graph when plotted:
Given that the Finance Toolkit is modular, you do not have to use the Toolkit functionality directly and can also call each functionality of the model separately. For example, this shows the output of using the model directly, specifying each parameter yourself.
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This release includes the Binomial Model, a mathematical model for pricing both American as well as European options. The Binomial Model is a discrete-time model that calculates the price of an option by creating a riskless hedge portfolio that replicates the payoff of the option. The model is based on the assumption that the price of the underlying asset follows a binomial distribution. The Binomial Model is a simple and intuitive model that is widely used in practice. It is also the basis for more complex models. See for an elaborate explanation the documentation as found here.
For example, when using the following code:
It returns a large DataFrame with the binomial tree for each company and each strike price around the current price (as defined by the
start_date
parameter).The resulting output is a DataFrame containing the tickers, strike prices and movements as the index and the time to expiration as the columns. The movements index contains the number of up movements and the number of down movements. The output is the binomial tree displayed in a table. E.g. when using 10 time steps, the table for each strike price from each company will contain the actual binomial tree as also depicted in the image as seen below. Find the documentation here.
When selecting for example Apple at a Strike Price of 140 you will get the actual Binomial Tree depicted as a table, this represents the tree you see in the image at the top.
The model contains parameters to lengthen the time steps, change the risk-free rate and the dividend yield but more importantly, make it possible to calculate the price of both American and European options as well as Call and Put options. For example, let's calculate the price of a American Put option with a strike price of 140 for Apple again:
Which returns the Option valuations for an American Put Option.
Under the hood of this model the stock prices are simulated based on up and down movements. These can be graphically depicted as a binomial tree and help in understanding the calculated option prices for each node in. More information about these stock price simulations can be found in the documentation here and as follows:
Which would return for Apple the following graph when plotted:
Given that the Finance Toolkit is modular, you do not have to use the Toolkit functionality directly and can also call each functionality of the model separately. For example, this shows the output of using the model directly, specifying each parameter yourself.
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