Dr John O'Hara
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Email
johara@essex.ac.uk -
Telephone
+44 (0) 1206 876510
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Location
STEM 5.35, Colchester Campus
Profile
Biography
I was an undergraduate pure mathematics major at the New University of Ulster. I completed my PGCE (in Education) and MSc (probability theory in Hilbert spaces) at Queen’s University, Belfast. My PhD was in the theory of differential equations, completed at the University of the Witwatersrand, Johannesburg South Africa. Before coming to the University of Essex (2010-present) I worked at several universities in Southern Africa. I was the Director of CCFEA (Centre for Computational Finance and Economic Agents in the School of Computer Science and Electronic Engineering). I am also a research fellow at the School for Data Science and Computational Thinking, at Stellenbosch University, and an Honorary Associate Professor at UCT, South Africa. My recent research interests include financial mathematics and machine learning in finance. I am a member of the London Mathematical Society and a Fellow of the Institute of Mathematics and its Applications.
Qualifications
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PhD University of the Witwatersrand, (1991)
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MSc Queen's University Belfast, (1981)
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PGCE Queen's University Belfast, (1977)
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BSc University of Ulster, (1976)
Appointments
University of Essex
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Deputy Director, CSEE, CCFEA (1/1/2010 - 1/10/2019)
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Director, CCFEA, University of Essex (1/10/2019 - 31/8/2021)
Research and professional activities
Research interests
The study of differential equations in finance
We use Lie symmetry methods to obtain analytic solutions to partial differential equations associated with the pricing of various financial derivatives.
The application of artificial intelligence in finance.
The construction of volatility surfaces in illiquid markets. The pricing of exotic options. Strategies for risk management.
Current research
Using stochastic differential equations in finance.
In this project we use Lie symmetry methods to find solutions to stochastic differential equations. Starting with a stochastic version of the Black-Scholes-Merton equation we calculate the symmetries of the equation, infinitesimal operators, group invariance and a solution.
These ideas are applied to other equations in the debt market.
More information about this project
Use deep neural networks and other machine learning methodologies for financial time series analysis.
We use current advances in financial time series analysis and deep learning. In particular, applying LSTM for sequence learning.
Using directional changes for searching “Head and Shoulder” patterns
Using a directional change approach to describe the behaviour of the financial markets.
Teaching and supervision
Current teaching responsibilities
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Financial Mathematics (MA226)
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Financial Derivatives (MA320)
Current supervision
Previous supervision
Degree subject: Computational Finance
Degree type: Doctor of Philosophy
Awarded date: 24/6/2024
Degree subject: Computational Finance
Degree type: Doctor of Philosophy
Awarded date: 22/1/2024
Degree subject: Computational Finance
Degree type: Doctor of Philosophy
Awarded date: 21/8/2023
Degree subject: Computational Finance
Degree type: Doctor of Philosophy
Awarded date: 17/10/2022
Degree subject: Computational Finance
Degree type: Doctor of Philosophy
Awarded date: 30/3/2022
Degree subject: Computational Finance
Degree type: Doctor of Philosophy
Awarded date: 20/10/2021
Degree subject: Computational Finance
Degree type: Doctor of Philosophy
Awarded date: 14/11/2019
Degree subject: Computational Finance
Degree type: Doctor of Philosophy
Awarded date: 4/1/2019
Degree subject: Computational Finance
Degree type: Doctor of Philosophy
Awarded date: 14/10/2016
Degree subject: Computational Finance
Degree type: Doctor of Philosophy
Awarded date: 10/7/2015
Degree subject: Computational Finance
Degree type: Doctor of Philosophy
Awarded date: 18/12/2013
Publications
Journal articles (39)
Huang, C-S., O'Hara, JG. and Mataramvura, S., (2022). Highly Efficient Shannon Wavelet-based Pricing of Power Options under the Double Exponential Jump Framework with Stochastic Jump Intensity and Volatility. Applied Mathematics and Computation. 414, 126669-126669
Rukanda, GS., Govinder, KS. and O'Hara, J., (2022). Option pricing: the reduced-form SDE model. Journal of Difference Equations and Applications. 28 (4), 590-604
Li, S., Tsang, EPK. and O'Hara, J., (2022). Measuring relative volatility in high‐frequency data under the directional change approach. Intelligent Systems in Accounting, Finance and Management. 29 (2), 86-102
Rostamian, A. and O'Hara, JG., (2022). Event prediction within directional change framework using a CNN-LSTM model. Neural Computing and Applications. 34 (20), 17193-17205
Ibrahim, SNI., Díaz-Hernández, A., O'Hara, JG. and Constantinou, N., (2019). Pricing holder-extendable call options with mean-reverting stochastic volatility. ANZIAM Journal. 61 (4), 382-397
Kaibe, BC. and O’Hara, JG., (2019). Symmetry Analysis of an Interest Rate Derivatives PDE Model in Financial Mathematics. Symmetry. 11 (8), 1056-1056
Huang, C-S., O'Hara, JG. and Mataramvura, S., (2017). Efficient pricing of discrete arithmetic Asian options under mean reversion and jumps based on Fourier-cosine expansions. Journal of Computational and Applied Mathematics. 311, 230-238
Ibrahim, SNI., Ng, TW., O'Hara, JG. and Nawawi, A., (2017). Pricing holder-extendable options in a stochastic volatility model with an ornstein-uhlenbeck process. Malaysian Journal of Mathematical Sciences. 11 (1), 1-8
Ibrahim, SNI., O'Hara, JG. and Zaki, MSM., (2016). Pricing Formula for Power Options with Jump-Diffusion. Applied Mathematics and Information Sciences. 10 (4), 1313-1317
O’Hara, JG., Sophocleous, C. and Leach, PGL., (2015). Erratum to: The application of Lie point symmetries to the resolution of certain problems in financial mathematics with a terminal condition. Journal of Engineering Mathematics. 91 (1), 215-216
Charalambous, K., Sophocleous, C., O'Hara, JG. and Leach, PGL., (2015). A deductive approach to the solution of the problem of optimal pairs trading from the viewpoint of stochastic control with time‐dependent parameters. Mathematical Methods in the Applied Sciences. 38 (17), 4448-4460
Okelola, MO., Govinder, KS. and O'Hara, JG., (2015). Solving a partial differential equation associated with the pricing of power options with time‐dependent parameters. Mathematical Methods in the Applied Sciences. 38 (14), 2901-2910
Wang, H., O'Hara, JG. and Constantinou, N., (2015). A path-independent approach to integrated variance under the CEV model. Mathematics and Computers in Simulation. 109, 130-152
Ibrahim, SNI., O'Hara, JG. and Constantinou, N., (2014). Pricing Extendible Options Using the Fast Fourier Transform. Mathematical Problems in Engineering. 2014, 1-7
Ibrahim, S., O'Hara, JG. and Constantinou, N., (2014). Pricing Extendible Options Using the Fast Fourier Transform. Mathematical problems in engineering. 2014, creators-O=27Hara=3AJohn_G=3A=3A
O’Hara, JG., Sophocleous, C. and Leach, PGL., (2013). Application of Lie point symmetries to the resolution of certain problems in financial mathematics with a terminal condition. Journal of Engineering Mathematics. 82 (1), 67-75
Ibrahim, SNI., O’Hara, JG. and Constantinou, N., (2013). Risk-neutral valuation of power barrier options. Applied Mathematics Letters. 26 (6), 595-600
O’Hara, JG., Sophocleous, C. and Leach, PGL., (2013). Symmetry analysis of a model for the exercise of a barrier option. Communications in Nonlinear Science and Numerical Simulation. 18 (9), 2367-2373
Ibrahim, S., O'Hara, JG. and Constantinou, N., (2013). Pricing Power Options under the Heston Dynamics using the FFT. New Trends in Mathematical Sciences. 1 (1), 1-9
Caister, NC., Govinder, KS. and O'Hara, JG., (2011). Optimal system of Lie group invariant solutions for the Asian option PDE. Mathematical Methods in the Applied Sciences. 34 (11), 1353-1365
Sophocleous, C., O’Hara, JG. and Leach, PGL., (2011). Symmetry analysis of a model of stochastic volatility with time-dependent parameters. Journal of Computational and Applied Mathematics. 235 (14), 4158-4164
Sinkala, W., Leach, PGL. and O'Hara, JG., (2011). Embedding the Vasicek model into the Cox-Ingersoll-Ross model. Mathematical Methods in the Applied Sciences. 34 (2), 152-159
Pillay, E. and O’Hara, JG., (2011). FFT based option pricing under a mean reverting process with stochastic volatility and jumps. Journal of Computational and Applied Mathematics. 235 (12), 3378-3384
Sophocleous, C., O’Hara, JG. and Leach, PGL., (2011). Algebraic solution of the Stein–Stein model for stochastic volatility. Communications in Nonlinear Science and Numerical Simulation. 16 (4), 1752-1759
Caister, NC., Govinder, KS. and O’Hara, JG., (2011). Solving a nonlinear pde that prices real options using utility based pricing methods. Nonlinear Analysis: Real World Applications. 12 (4), 2408-2415
Naicker, V., O’Hara, JG. and Leach, PGL., (2010). A note on the integrability of the classical portfolio selection model. Applied Mathematics Letters. 23 (9), 1114-1119
Gounden, S. and O’Hara, JG., (2010). An analytic formula for the price of an American-style Asian option of floating strike type. Applied Mathematics and Computation. 217 (7), 2923-2936
Caister, NC., O'Hara, JG. and Govinder, KS., (2010). Solving the Asian Option PDE Using LIE Symmetry Methods. International Journal of Theoretical and Applied Finance. 13 (08), 1265-1277
Sinkala, W., Leach, PGL. and O'Hara, JG., (2008). Invariance properties of a general bond-pricing equation. Journal of Differential Equations. 244 (11), 2820-2835
Sinkala, W., Leach, PGL. and O'Hara, JG., (2008). Zero-coupon bond prices in the Vasicek and CIR models: Their computation as group-invariant solutions. Mathematical Methods in the Applied Sciences. 31 (6), 665-678
Sinkala, W., Leach, PGL. and O'Hara, JG., (2008). An optimal system and group-invariant solutions of the Cox-Ingersoll-Ross pricing equation. Applied Mathematics and Computation. 201 (1-2), 95-107
Leach, PGL., O'Hara, JG. and Sinkala, W., (2007). Symmetry-based solution of a model for a combination of a risky investment and a riskless investment. Journal of Mathematical Analysis and Applications. 334 (1), 368-381
O'Hara, J., (2007). Toward a Commodity Enterprise Middleware. Queue. 5 (4), 48-55
O’Hara, JG., Pillay, P. and Xu, H-K., (2006). Iterative approaches to convex feasibility problems in Banach spaces. Nonlinear Analysis: Theory, Methods & Applications. 64 (9), 2022-2042
O'Hara, JG., Pillay, P. and Xu, H-K., (2004). Iterative Approaches to Convex Minimization Problems. Numerical Functional Analysis and Optimization. 25 (5-6), 531-546
O'Hara, JG., Pillay, P. and Xu, H-K., (2003). Iterative approaches to finding nearest common fixed points of nonexpansive mappings in Hilbert spaces. Nonlinear Analysis: Theory, Methods & Applications. 54 (8), 1417-1426
O'Hara, J. and Payne, VF., (1998). Construction of separating functions for the quasi—linear differential equation (py′)′+qy=0. Applicable Analysis. 69 (1-2), 118-126
O'Hara, JG., (1996). On an Oscillation Criterion for a Second Order Linear Quasi-Differential Equation. Journal of the London Mathematical Society. 54 (2), 251-260
O'Hara, JG., (1996). A Comparison Theorem for a Second Order Linear Quasi-Differential Equation. Journal of the London Mathematical Society. 53 (1), 118-126
Conferences (5)
O'Hara, J. and Huang, C-S., Recent Advances in Fourier Transform Methods for Computational Finance and Insurance
Gong, Z., Ventre, C. and O'Hara, J., (2021). The efficient hedging frontier with deep neural networks
Gong, Z., Ventre, C. and O'Hara, J., (2020). Classifying high-frequency FX rate movements with technical indicators and inception model
Chong, KY. and O'Hara, JG., (2019). Lie symmetry analysis of a fractional Black-Scholes equation
Ibrahim, SN., O'Hara, JG. and Constantinou, N., (2012). Power option pricing via Fast Fourier Transform
Reports and Papers (1)
Huang, C-S., O'Hara, JG. and Mataramvura, S., Highly Efficient Option Valuation Under the Double Jump Framework with Stochastic Volatility and Jump Intensity Based on Shannon Wavelet Inverse Fourier Technique
Grants and funding
2023
KTP re: Fraud Detection with Ticker Ltd
Innovate UK (formerly Technology Strategy Board)
