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Code for "Model-free price bounds under dynamic option trading"

Ariel Neufeld, Julian Sester

Abstract

In this paper we extend discrete time semi-static trading strategies by also allowing for dynamic trading in a finite amount of options, and we study the consequences for the model-independent super-replication prices of exotic derivatives. These include duality results as well as a precise characterization of pricing rules for the dynamically tradable options triggering an improvement of the price bounds for exotic derivatives in comparison with the conventional price bounds obtained through the martingale optimal transport approach.

Preprint

Can be found here

Content

This folder contains:

functions.R:, All Functions for Computation of No-Statistical Arbitrage Bounds and the corresponding replication strategies are defined here.

This folder contains:

  1. Example_3_1.ipynb, Contains the Code associated to Example 3.1.
  2. Example_3_2.ipynb, Contains the Code associated to Example 3.2.
  3. Example_3_3.ipynb, Contains the Code associated to Example 3.3.
  4. Example_3_4.ipynb, Contains the Code associated to Example 3.4. without data of the call options.

Data

Note that the stock data for the examples cannot be provided for legal reasons.

License

MIT License

Copyright (c) 2021 Julian Sester

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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Model-free price bounds under dynamic option trading

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