# Registered Data

Contents

- 1 [CT176]
- 1.1 [01216] Neural network in option pricing
- 1.2 [02592] Pricing American barrier options with transaction costs
- 1.3 [00964] The Valuation of Real Options for Risky Barrier to Entry with Hybrid Stochastic and Local Volatility and Stochastic Investment Costs
- 1.4 [02334] A generalized integral equation formulation for pricing American options under regime-switching model
- 1.5 [02330] Representation Learning for Continuous Single-cell Biology with Graph Neural Networks

# [CT176]

**Session Time & Room****Classification**

## [01216] Neural network in option pricing

**Session Time & Room**:__4E__(Aug.24, 17:40-19:20) @__D505__**Type**: Contributed Talk**Abstract**: Black-Scholes model is the universally accepted model for computing option prices. While its is robust and easy to use, it has many flaws. Moreover, it failed spectacularly in 1987 during the wall street crash. This has led to proliferation of many extensions to the Black-Scholes model. Most extensions focus on relaxing the constant volatility assumption by incorporating randomness in the volatility. Whilst it provides slightly better estimation to option prices, it is computationally expensive to implement. Moreover, most of these models do not have closed-form solutions With advancement in computational techniques, neural network has been increasingly used to price options. Not only, does it outperform conventional stochastic volatility models, it does not require assumption on the statistical characteristics of assets and volatility distribution. A typical neural network consists of three layers: input, hidden, and output. It uses a supervised learning method based on the generalisation of the least mean square error (LMS) algorithm. A gradient descent method is used to minimise the cost function, which is the mean square difference between the target and actual net output. More advanced neural networks (deep learning architectures), such as a Recurrent Neural Network (RNN) and its variant Long Short-Term Memory (LSTM), are useful for taking care of the time-series nature of financial data. The general architecture of the convolutional neural network-based LSTM model includes an input layer, one or more convolutional layers, long short-term memory layer(s), dense layer(s), and an output layer. In this research, we will attempt to predict Strait Times Index (STI) which is one of the most regularly traded options in Singapore Exchange (SGX). After pre-processing and cleaning the data, the input (stock price, time to maturity and volatility and output (option prices) , variables will be extracted for training and testing the models. Various hyperparameters (optimizers, learning rate, hidden layers, activation functions, etc.) will be optimised to generate the best model for the prediction of the option pricing. A comparison of the accuracy of the prediction of option pricing will be performed for three models, namely convolutional neural network-based LSTM, Multilayer Perceptron neural network N and the Black Scholes option pricing model. Different metrics (root mean squared error, mean absolute error, and mean absolute percentage error) will be used to compare the performance of the models.**Classification**:__91G15__,__91G20__**Format**: Talk at Waseda University**Author(s)**:**Abby Chee Hong Tan**(Universiti Brunei Darussalam)

## [02592] Pricing American barrier options with transaction costs

**Session Time & Room**:__4E__(Aug.24, 17:40-19:20) @__D505__**Type**: Contributed Talk**Abstract**: When transaction costs in trading underlying stocks are considered, far more modelling effort is needed for pricing options, as a unique fair price between the holder and writer no longer exists. It becomes even more complicated for American and exotic options. In this talk, we shall discuss the valuation of American barrier options with transaction costs and examine the impact of transaction costs on option pricing, particularly on how they affect the optimal exercise boundary.**Classification**:__91G20__,__60G40__,__Mathematical finance__**Format**: Talk at Waseda University**Author(s)**:**Xiaoping Lu**(University of Wollongong)

## [00964] The Valuation of Real Options for Risky Barrier to Entry with Hybrid Stochastic and Local Volatility and Stochastic Investment Costs

**Session Time & Room**:__4E__(Aug.24, 17:40-19:20) @__D505__**Type**: Contributed Talk**Abstract**: Real options are sorts of investment choices which support agents in making better decisions in management strategic cases as well as reducing uncertainty in investment simultaneously. In this paper, we present the new model for investors to handle uncertain environments in investment flexibly: First, we adopt a hybrid stochastic and local volatility model to efficiently describe the external uncertain environment affecting the value of the project in decision making cases, and we set up the investment cost as geometric Brownian motion to illustrate the value of the opportunity costs which arise from things given up by choosing to invest in complex decision making circumstances. We derive partial differential equations for the value of real options and then use asymptotic analysis to obtain analytical solutions for that of the real options. In addition, we analyze the price accuracy of the approximated formulas compared to the solutions obtained from Monte-Carlo simulation. Finally, we investigate the effects of various parameters related to stochastic volatility on real options numerically to observe economic implications.**Classification**:__91G20__**Format**: Talk at Waseda University**Author(s)**:**Donghyun Kim**(Pusan National University)- Yong Hyun Shin (Sookmyung Women's University)
- Ji-Hun Yoon (Pusan National University)

## [02334] A generalized integral equation formulation for pricing American options under regime-switching model

**Session Time & Room**:__4E__(Aug.24, 17:40-19:20) @__D505__**Type**: Contributed Talk**Abstract**: In this paper, we present a generalized integral equation formulation for American put options under regime-switching model, with a goal of improving computational efficiency in mind, particularly when the number of regimes, $n$ is large. Given that the integral equation approach is characterized with its excellent trade off between maximizing analytical tractability and minimizing numerical discretization, our achieved high efficiency is based on a newly proved theorem, which facilitates the decoupling of an originally simultaneously involved $n$-PDEs so that they can be solved recursively at the numerical solution stage. While some numerical examples are provided to demonstrate the implementation of the new approach and its efficiency, it is anticipated that the very same theorem can be used to reduce the computational burden if other numerical approaches are adopted.**Classification**:__91G20__,__91-10__**Format**: Talk at Waseda University**Author(s)**:**Yawen Zheng**(University of Wollongong)- Song-Ping Zhu (University of Wollongong)

## [02330] Representation Learning for Continuous Single-cell Biology with Graph Neural Networks

**Session Time & Room**:__4E__(Aug.24, 17:40-19:20) @__D505__**Type**: Contributed Talk**Abstract**: Single-cell RNA sequencing provides high-resolution transcriptomics to study cellular dynamic processes, yet its high-dimensionality, sparsity, and noises undermine the performance of downstream analysis. We propose a deep learning framework based on Variational Graph AutoEncoder to learn a low-dimensional representation that preserves global information and local continuity. By applying pseudotemporal ordering to the extracted features, we show that the model accurately preserves the dynamic cell trajectories of real and synthetic scRNA-seq datasets.**Classification**:__92B20__,__68T05__,__Machine Learning, Bioinformatics__**Format**: Talk at Waseda University**Author(s)**:**Chengkai Yang**(The University of Tokyo)