Bjerksund-Stensland approximation is an alternative to the Baron-Adesi Whaley approximation for American options pricing formula under Black-Scholes.

The module implementing this method should live under tf_quant_finance/volatility/american_option.py. It should support both puts and calls. Tests should be in american_option_test.py in the same folder.

I'm trying to replicate the TARF payoff from this paper. So far, i've been able to write a payoff that can be evaluated with MC and GPU, but i get an error with the XLA compilation. https://colab.research.google.com/github/arthurpham/google_colab/blob/7d5715c2b0f988c8d7d544fea0ff741e63272056/TARF_MC_Performance_TQF.ipynb I understand that the payoff code style might not be the best, but i wasn't able to find an example of a path-dependent payoff with MC. Any pointer would be helpful.

---------------------------------------------------------------------------
InvalidArgumentError                      Traceback (most recent call last)
<ipython-input-7-945d7282d2b1> in <module>()
      1 device = "/gpu:0"
      2 with tf.device(device):
----> 3     tarf_price = price_eu_options_xla(strikes, spot, sigma)
      4     print('price', tarf_price)

1 frames
/usr/local/lib/python3.7/dist-packages/tensorflow/python/eager/execute.py in quick_execute(op_name, num_outputs, inputs, attrs, ctx, name)
     53     ctx.ensure_initialized()
     54     tensors = pywrap_tfe.TFE_Py_Execute(ctx._handle, device_name, op_name,
---> 55                                         inputs, attrs, num_outputs)
     56   except core._NotOkStatusException as e:
     57     if name is not None:

InvalidArgumentError: Detected unsupported operations when trying to compile graph __inference_price_eu_options_9107[_XlaMustCompile=true,config_proto=6001324581131673121,executor_type=11160318154034397263] on XLA_GPU_JIT: TensorListReserve (No registered 'TensorListReserve' OpKernel for XLA_GPU_JIT devices compatible with node {{function_node __inference_while_fn_9086}}{{node while_init/TensorArrayV2_7}}
	 (OpKernel was found, but attributes didn't match) Requested Attributes: element_dtype=DT_VARIANT, shape_type=DT_INT32){{function_node __inference_while_fn_9086}}{{node while_init/TensorArrayV2_7}}
The op is created at: 
File "/usr/lib/python3.7/runpy.py", line 193, in _run_module_as_main
  "__main__", mod_spec)
File "/usr/lib/python3.7/runpy.py", line 85, in _run_code
  exec(code, run_globals)
File "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py", line 16, in <module>
  app.launch_new_instance()
File "/usr/local/lib/python3.7/dist-packages/traitlets/config/application.py", line 846, in launch_instance
  app.start()
File "/usr/local/lib/python3.7/dist-packages/ipykernel/kernelapp.py", line 499, in start
  self.io_loop.start()
File "/usr/local/lib/python3.7/dist-packages/tornado/platform/asyncio.py", line 132, in start
  self.asyncio_loop.run_forever()
File "/usr/lib/python3.7/asyncio/base_events.py", line 541, in run_forever
  self._run_once()
File "/usr/lib/python3.7/asyncio/base_events.py", line 1786, in _run_once
  handle._run()
File "/usr/lib/python3.7/asyncio/events.py", line 88, in _run
  self._context.run(self._callback, *self._args)
File "/usr/local/lib/python3.7/dist-packages/tornado/ioloop.py", line 758, in _run_callback
  ret = callback()
File "/usr/local/lib/python3.7/dist-packages/tornado/stack_context.py", line 300, in null_wrapper
  return fn(*args, **kwargs)
File "/usr/local/lib/python3.7/dist-packages/zmq/eventloop/zmqstream.py", line 536, in <lambda>
  self.io_loop.add_callback(lambda: self._handle_events(self.socket, 0))
File "/usr/local/lib/python3.7/dist-packages/zmq/eventloop/zmqstream.py", line 452, in _handle_events
  self._handle_recv()
File "/usr/local/lib/python3.7/dist-packages/zmq/eventloop/zmqstream.py", line 481, in _handle_recv
  self._run_callback(callback, msg)
File "/usr/local/lib/python3.7/dist-packages/zmq/eventloop/zmqstream.py", line 431, in _run_callback
  callback(*args, **kwargs)
File "/usr/local/lib/python3.7/dist-packages/tornado/stack_context.py", line 300, in null_wrapper
  return fn(*args, **kwargs)
File "/usr/local/lib/python3.7/dist-packages/ipykernel/kernelbase.py", line 283, in dispatcher
  return self.dispatch_shell(stream, msg)
File "/usr/local/lib/python3.7/dist-packages/ipykernel/kernelbase.py", line 233, in dispatch_shell
  handler(stream, idents, msg)
File "/usr/local/lib/python3.7/dist-packages/ipykernel/kernelbase.py", line 399, in execute_request
  user_expressions, allow_stdin)
File "/usr/local/lib/python3.7/dist-packages/ipykernel/ipkernel.py", line 208, in do_execute
  res = shell.run_cell(code, store_history=store_history, silent=silent)
File "/usr/local/lib/python3.7/dist-packages/ipykernel/zmqshell.py", line 537, in run_cell
  return super(ZMQInteractiveShell, self).run_cell(*args, **kwargs)
File "/usr/local/lib/python3.7/dist-packages/IPython/core/interactiveshell.py", line 2718, in run_cell
  interactivity=interactivity, compiler=compiler, result=result)
File "/usr/local/lib/python3.7/dist-packages/IPython/core/interactiveshell.py", line 2822, in run_ast_nodes
  if self.run_code(code, result):
File "/usr/local/lib/python3.7/dist-packages/IPython/core/interactiveshell.py", line 2882, in run_code
  exec(code_obj, self.user_global_ns, self.user_ns)
File "<ipython-input-7-945d7282d2b1>", line 3, in <module>
  tarf_price = price_eu_options_xla(strikes, spot, sigma)
File "<ipython-input-5-1d20baab715c>", line 89, in price_eu_options
  payoffs = tf.vectorized_map(my_function, reshaped_paths) [Op:__inference_price_eu_options_9107]

Formulas for pricing a Barrier option under Black-Scholes model is of interest. (See, e.g., Section 26.9 of Hull(2018), Options, Futures, and Other Derivatives, 9th edition).

The module implementing this method should live under tf_quant_finance/volatility/barrier_option.py. It should support both puts (up-and-in put, down-and-out put) and calls (down-in call, up-and-out call). Tests should be in barrier_option_test.py in the same folder.

The change is to implement a jupyter notebook example for curve fitting. It covers

• curve fitting of discount rates by OIS

• curve fitting of discount rates by LIBOR fix, Eurodollar futures and swap rates

Motiviation/Rational

While the intent is to add both of the Bjerksund-Stensland option pricing models for american exercise options, this pull request is for the 1993 model, with the 2002 model to follow shortly after.

Testing

The primary source used is the description of the 1993 model in the paper on the 2002 model here. Included in the paper are four tables with values for the 1993 model (referenced as "flat boundary approximation"). A test was run checking all of the values (source code can be provided upon request):

Closed Form Valuation of American Options, 2002
Table 1, pg. 9 - 1993 model
Section 1, Calls:  [ 0.03  0.57  3.49 10.32 20.  ]  Puts:  [20.41 11.25  4.4   1.12  0.18]
Section 2, Calls:  [ 0.03  0.57  3.46 10.29 20.  ]  Puts:  [20.22 11.14  4.35  1.11  0.18]
Section 3, Calls:  [ 1.05  3.25  7.37 13.47 21.23]  Puts:  [21.44 13.91  8.27  4.52  2.29]
Section 4, Calls:  [ 0.21  1.34  4.65 10.94 20.  ]  Puts:  [20.95 12.63  6.37  2.65  0.92]
Table 2, pg. 10 - 1993 model
Section 1, Calls:  [ 0.05  0.85  4.44 11.66 20.9 ]  Puts:  [20.   10.19  3.51  0.78  0.11]
Section 2, Calls:  [ 0.05  0.84  4.4  11.55 20.69]  Puts:  [20.   10.17  3.49  0.77  0.11]
Section 3, Calls:  [ 1.29  3.82  8.35 14.8  22.71]  Puts:  [20.53 12.91  7.42  3.93  1.93]
Section 4, Calls:  [ 0.41  2.18  6.5  13.42 22.06]  Puts:  [20.   10.7   4.7   1.71  0.52]
Table 3, pg. 11 - 1993 model
Section 1, Puts:  [20.   10.01  3.16  0.65  0.09]
Section 2, Puts:  [20.   10.    2.86  0.54  0.07]
Section 3, Puts:  [20.28 12.48  7.04  3.66  1.77]
Section 4, Puts:  [20.   10.24  4.11  1.37  0.39]
Table 4, pg. 12 - 1993 model
Section 1, Calls:  [ 2.3   4.71  8.44 13.74 20.85]  Puts:  [25.61 20.04 15.47 11.78  8.87]
Section 2, Calls:  [ 3.95  7.2  11.64 17.24 23.93]  Puts:  [22.12 16.14 11.64  8.31  5.89]
Section 3, Calls:  [16.75 22.25 28.31 34.84 41.77]  Puts:  [28.42 23.97 20.34 17.34 14.86]
Section 4, Puts:  [20.   11.67  6.9   4.12  2.48]

All of the values match, with the only exception being those in Table 4, Section 3. Confirming the values using online calculators, such as this one here, led to the conclusion that the values in Table 4, Section 3 are not correct - but I would appreciate the input of others.

This PR is in draft status as I still need to add tests to american_option_test.py.

Binomial options pricing models like Cox-Ross-Rubinstein have been widely used since they are able to handle a variety of conditions for which other models cannot easily be applied proving themselves to be more accurate, particularly for longer-dated options on securities with dividend payments.

Remedy the incorrect display of a formula in an example notebook. (Line changing within the LaTeX codes refrains the formula from being displayed correctly.)

when cloning, the following warning pops up:

warning: the following paths have collided (e.g. case-sensitive paths on a case-insensitive filesystem) and only one from the same colliding group is in the working tree:

'api_docs/tf_quant_finance/datetime/Month.md' 'api_docs/tf_quant_finance/datetime/month.md'

Hi,

I have just cloned this project and find that Month.md and month.md in api_docs/tf_quant_finance/datetime/ collide on my macOS. I could not pull recent merges. The best solution is to reformat my local APFS filesystem. But I think reformatting filesystem seems not a good choice. I guess api_docs may be generated automatically. However, it would be nice if the api and the markdown file could change to another name. And it would benefit other developers who want to clone the project into their macOS filesystem.

Thanks!

This pull requests adds the Bjerksund-Stensland 2002 option pricing model, which closes #5.

Tests are included which mirror the tables in the reference paper. Additional testing in both eager and deferred (graph) mode were conducted with visual inspection of the output of the code. All tests were successful.

This pull request fixes #50.

Motivation/Rational

The argument for dividends across different option pricing models used two names when only one was needed. This pull request updates the files using continuous_dividends to instead use dividend_rates. This makes it easier for end-users to reuse code when using the different option pricing models.

Explanation of Changes

As requested in issue #50, deprecation decorators were used to alert users to the change in argument names. All argument names in the tf_quant_finance/black_scholes/ directory and sub-directories for continuous_dividends were changed to dividend_rates.

Testing

Many of the methods changed start with the variadic argument (*), which caused test to fail as Bazel would not recognize that the deprecated argument continuous_dividends was in the argument list, causing an error. When the variadic argument was removed, tests completed successfully.

Hi! The main page mentions: tf-quant-finance: Open mailing list for discussion and questions of this library. However, the group isn't findable and subscribing via email reveals its settings are "Invite Only". I would suggest to remedy this by either adjusting the settings or updating the info on the main page to remove the list. Thank you,

As of QuantLib 1.28 the default constructor when calling ql.Thirty360() is no longer available in the underlying C++ library, and so a BondBasis must be supplied. Otherwise a TypeError will be thrown when executing these notebook cells:

TypeError                                 Traceback (most recent call last)
[<ipython-input-17-0acd484f2084>](https://localhost:8080/#) in <module>
     35 calculation_date = ql.Date(1, 1, 2010)
     36 maturity_date = ql.Date(1, 1, 2011)
---> 37 day_count = ql.Thirty360()
     38 calendar = ql.NullCalendar()
     39 

[/usr/local/lib/python3.8/dist-packages/QuantLib/QuantLib.py](https://localhost:8080/#) in __init__(self, *args)
   3479 
   3480     def __init__(self, *args):
-> 3481         _QuantLib.Thirty360_swiginit(self, _QuantLib.new_Thirty360(*args))
   3482     __swig_destroy__ = _QuantLib.delete_Thirty360
   3483 

TypeError: Wrong number or type of arguments for overloaded function 'new_Thirty360'.
  Possible C/C++ prototypes are:
    QuantLib::Thirty360::Thirty360(QuantLib::Thirty360::Convention,Date const &)
    QuantLib::Thirty360::Thirty360(QuantLib::Thirty360::Convention)

For details see: https://stackoverflow.com/a/74336038/1773216

Pricing discrete geometric asians under Heston volatility, using the method described by B. Kim, J. Kim, J. Kim & I. S. Wee in "A Recursive Method for Discretely Monitored Geometric Asian Option Prices"

Hi,

I noticed a problem with the time grid in euler_sample when XLA compilation (with dynamic shape for times) is used.

https://colab.research.google.com/drive/1kg8RChmJ3TxdONBHE1lIdCAmZKIXwGcY#scrollTo=pohADCcoTZMh

Thank you

Hi guys,

In the "Monte Carlo via Euler Scheme" example you compare TF with QuantLib pricing and conclude that TF finance is x100 times faster(or more).

I want to note that in QL you evolve 100 time steps of Log Normal process, but in TF you work in log space and only apply exp() at the end. I agree QL may not be very fast, but in this example you compare 100 exponents per path in QL to just 1 exponent in TF...

Thank you!