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https://github.com/brendanbignell/cuda_montecarlooptionpricer

CUDA Monte Carlo Barrier Option Pricing Demo & Jupyer lab ML models
https://github.com/brendanbignell/cuda_montecarlooptionpricer

cuda deep-learning ml pytorch quantitative-finance xgboost-regression

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CUDA Monte Carlo Barrier Option Pricing Demo & Jupyer lab ML models

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README 

        
![CoverImage](https://github.com/brendanbignell/CUDA_MonteCarloOptionPricer/blob/master/images/Barriers-DALL-E.png)



# CUDA Barrier Option Pricing & ML Model Training



This a demo of how Barrier Options can be priced using Monte Carlo Simulations running on a cluster of NVidia GPUs.  The option pricing results are used to train a machine learning models to predict the price of the Barrier Options. The idea being that a trained ML model could be used to price options more quickly than running a Monte Carlo simulation.  Tests show a XGBoost Gradient Boosted Decision Tree model can predict more than 400K barrier option prices per second without given much though to optimization.  Later tests investigate using deep learning models using the PyTorch framework.



Note: Not much effort was taken to validate the calculated prices.  The main goal was to generate a large dataset of barrier option prices to train ML models and understand CUDA better.



The demo constists of two parts:



## 1. CUDA Monte Carlo Simulation for pricing Barrier Options 	 

   

   The following barrier option types are supported:



	- Up-and-Out, Down-and-Out, Up-and-In & Down-and-In



	- European & American Exercise (American options use the Longstaff-Schwartz algorithm)



	- Call & Put Options



	The main() function in CUDA_MonteCarloOptionPricer.cu is used to drive batch pricing of random portfolios of Barrier Options.



   The option parameters and pricing results are written to a CSV file. Sample 100K and 1M output files are included in the repo.  A 10M barrier options file was generated and used to train the final versions of the ML models.



   ![Create Barriers](https://github.com/brendanbignell/CUDA_MonteCarloOptionPricer/blob/master/images/CreateBarriers.png)



## 2. Python Jupyter Notebooks 



### 2.1.  barrier_quick_ml_model_eval.ipynb

Demonstrates how to train a machine learning models to predict the price of Barrier Options. For this example Support Vector Machine (SVM), Random Forest and XGBoost GBDT models were initiially evaluated. The XGBoost model was selected for further training and testing as the initial results seemed the most promising. 



   ![Model Eval](https://github.com/brendanbignell/CUDA_MonteCarloOptionPricer/blob/master/images/QuickModelEvals.png)



### 2.2.  barrier_xgboost.ipynb



XGBoost Gradient Boosted Decision Tree Models were trained on 10 million barrier options. Model accuracy statistics are calculated, Mathpoltlib and Ploty charts are then used to visualize the model performance.

 

 ![European Barriers](https://github.com/brendanbignell/CUDA_MonteCarloOptionPricer/blob/master/images/EuropeanBarriers.png)



 ![American Barriers](https://github.com/brendanbignell/CUDA_MonteCarloOptionPricer/blob/master/images/AmericanBarriers.png)



 ### 2.3.  barrier_dl_pytorch.ipynb



 First attempt at using PyTorch to train a Deep Learning model to predict the price of Barrier Options. 



 ![PyTorch Barriers](https://github.com/brendanbignell/CUDA_MonteCarloOptionPricer/blob/master/images/PyTorchBarriers.png)



 ### 2.4.  barrier_dl_pytorch_enhanced.ipynb



  Updated model architecture and multi-gpu training.  However, the results are currently worse than the barrier_dl_pytorch model.

 

  ![PyTorch Barriers Enhanced](https://github.com/brendanbignell/CUDA_MonteCarloOptionPricer/blob/master/images/PyTorchBarriersEnhanced.png)



 ## 3. Further Work



 #### 3.1. Option Paramters

 The random option parameters could be chosen more wisely to better represent real world options.



 #### 3.2. Results Analysis

 Further analysis of ML model prediction results.  E.g. Outliers and why are American options predicted better than European options?  There is surely a lot that can be done to improve the model accuracy.



 #### 3.3. Hyperparameter tuning

 E.g. Using a grid of heuristic driven search of the XGBoost model hyperparameters to improve accuracy.



 ### 3.4. Alternate Models

 More advanced ML models and ensembles of models could be evaluated.



 ### 3.5. Code refinement and optimization

 The code was quickly hacked together as a proof of concept and pretty much all of it could be improved. E.g. The CUDA code could be optimized to run faster, the Python code could be refactored to be more readable and efficient.



 ### 3.6. Sources of errors

 BarrierType, ExerciseType, OptionType are encoded as integers.  However only BarrierType has more than two unique values and should be one-hot encoded, however some models such as XGBoost do not require this. One-hot encoding is used in the PyTorch models.



 ### 3.7. Feature Engineering

 The current model uses the option parameters as input features.  Other features could be engineered from the option parameters to improve model accuracy.  E.g. Moneyness.  Features such as initial option greeks could be calculated and used as input features, but I suspect these would not be useful as they can change dramatically over the life of the option.



Rather than only using the average of barrier option pricing paths to calculate the price we could also capture a bunch of statistics such as the stdev of the price paths, quantiles etc. and use these as additional model features.  Perhaps these statistics could be used to measure the confidence of the price.