# Registered Data

Contents

- 1 [CT176]
- 1.1 [01216] Neural network in option pricing
- 1.2 [00964] The Valuation of Real Options for Risky Barrier to Entry with Hybrid Stochastic and Local Volatility and Stochastic Investment Costs
- 1.3 [02334] A generalized integral equation formulation for pricing American options under regime-switching model
- 1.4 [02592] Pricing American barrier options with transaction costs
- 1.5 [02650] Endogenous Network Valuation Adjustment and the Systemic Term Structure in a Dynamic Interbank Model

# [CT176]

## [01216] Neural network in option pricing

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**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__**Author(s)**:**Abby Chee Hong Tan**(Universiti Brunei Darussalam)

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

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**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__**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 Date & Time**: 4E (Aug.24, 17:40-19:20)**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__**Author(s)**:**Yawen Zheng**(University of Wollongong)- Song-Ping Zhu (University of Wollongong)

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

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**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__**Author(s)**:**Xiaoping Lu**(University of Wollongong)

## [02650] Endogenous Network Valuation Adjustment and the Systemic Term Structure in a Dynamic Interbank Model

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: We introduce an interbank network model with stochastic dynamics in order to study the yield curve of bank debt under an endogenous network valuation adjustment. This entails a forward-backward approach in which future probabilities of default are required to determine the present value of debt. As an interesting consequence, systemic risk can emerge from current expectations about future distress and inverted term structures may appear. Numerical case studies are presented to demonstrate the financial implications.**Classification**:__91G45__**Author(s)**:**Andreas Sojmark**(London School of Economics)- Andreas Sojmark (London School of Economics)