Conall O'Sullivan

Adaptive genetic programming for option pricing

Genetic Programming (GP) is an automated computational programming methodology, inspired by the workings of natural evolution techniques. It has been applied to solve complex problems in multiple domains including finance. This paper illustrates the application of an adaptive form of GP, where the probability of crossover and mutation is adapted dynamically during the GP run, to the important real-world problem of options pricing. The tests are carried out using market option price data and the results illustrate that the new method yields better results than are obtained from GP with fixed crossover and mutation rates. The developed method has potential for implementation across a range of dynamic problem environments.

On the acceleration of explicit finite difference methods for option pricing

Implicit finite difference methods are conventionally preferred over their explicit counterparts for the numerical valuation of options. In large part the reason for this is a severe stability constraint known as the Courant–Friedrichs–Lewy (CFL) condition which limits the latter classs efficiency. Implicit methods, however, are difficult to implement for all but the most simple of pricing models, whereas explicit techniques are easily adapted to complex problems. For the first time in a financial context, we present an acceleration technique, applicable to explicit finite difference schemes describing diffusive processes with symmetric evolution operators, called Super-Time-Stepping. We show that this method can be implemented as part of a more general approach for non-symmetric operators. Formal stability is thereby deduced for the exemplar cases of European and American put options priced under the Black–Scholes equation. Furthermore, we introduce a novel approach to describing the efficiencies of finite difference schemes as semi-empirical power laws relating the minimal real time required to carry out the numerical integration to a solution with a specified accuracy. Tests are described in which the method is shown to significantly ameliorate the severity of the CFL constraint whilst retaining the simplicity of the underlying explicit method. Degrees of acceleration are achieved yielding comparable, or superior, efficiencies to a set of benchmark implicit schemes. We infer that the described method is a powerful tool, the explicit nature of which makes it ideally suited to the treatment of symmetric and non-symmetric diffusion operators describing complex financial instruments including multi-dimensional systems requiring representation on decomposed and/or adaptive meshes.

Quantum-Inspired Evolutionary Algorithms for Calibration of the VG Option Pricing Model

Quantum effects are a natural phenomenon and just like evolution, or immune systems, can serve as an inspiration for the design of computing algorithms. This study illustrates how a quantum-inspired evolutionary algorithm can be constructed and examines the utility of the resulting algorithm on Option Pricing model calibration. The results from the algorithm are shown to be robust and comparable to those of other algorithms.

Quantum-inspired evolutionary algorithms for financial data analysis

This paper describes a real-valued quantum-inspired evolutionary algorithm (QIEA), a new computational approach which bears similarity with estimation of distribution algorithms (EDAs). The study assesses the performance of the QIEA on a series of benchmark problems and compares the results with those from a canonical genetic algorithm. Furthermore, we apply QIEA to a finance problem, namely non-linear principal component analysis of implied volatilities. The results from the algorithm are shown to be robust and they suggest potential for useful application of the QIEA to high-dimensional optimization problems in finance.

Option pricing model calibration using a real-valued quantum-inspired evolutionary algorithm

Quantum effects are a natural phenomenon and just like evolution, or immune processes, can serve as an inspiration for the design of computing algorithms. This study illustrates how a real-valued quantum-inspired evolutionary algorithm(QEA) can be constructed and examines the utility of the resulting algorithm on an important real-world problem, namely the calibration of an Option Pricing model. The results from the algorithm are shown to be robust and sensitivity analysis is carried out on the algorithm parameters, suggesting that there is useful potential to apply QEA to this domain.

Pricing European And American Options In The Heston Model With Accelerated Explicit Finite Differencing Methods

We present an acceleration technique, effective for explicit finite difference schemes describing diffusive processes with nearly symmetric operators, called Super-Time-Stepping (STS). The technique is applied to the two-factor problem of option pricing under stochastic volatility. It is shown to significantly reduce the severity of the stability constraint known as the Courant-Friedrichs-Lewy condition whilst retaining the simplicity of the chosen underlying explicit method.For European and American put options under Hestons stochastic volatility model we demonstrate degrees of acceleration over standard explicit methods sufficient to achieve comparable, or superior, efficiency to benchmark implicit schemes. We conclude that STS accelerated methods are powerful numerical tools for the pricing of options which inherit the simplicity of explicit methods whilst achieving high accuracy at low computational cost and offer a compelling alternative to conventional implicit techniques.

Realised volatility forecasting: A genetic programming approach

Forecasting daily returns volatility is crucial in finance. Traditionally, volatility is modelled using a time-series of lagged information only, an approach which is in essence a theoretical. Although the relationship of market conditions and volatility has been studied for decades, we still lack a clear theoretical framework to allow us to forecast volatility, despite having many plausible explanatory variables. This setting of a data-rich but theory-poor environment suggests a useful role for powerful model induction methodologies such as Genetic Programming. This study forecasts one-day ahead realised volatility (RV) using a GP methodology that incorporates information on market conditions including trading volume, number of transactions, bid-ask spread, average trading duration and implied volatility. The forecasting result from GP is found to be significantly better than that of the benchmark model from the traditional finance literature, the heterogeneous autoregressive model (HAR).

A genetic programming approach for delta hedging

Effective hedging of derivative securities is of paramount importance to derivatives investors and to market makers. The standard approach used to hedge derivative instruments is delta hedging. In a Black-Scholes setting, a continuously rebalanced delta hedged portfolio will result in a perfect hedge with no associated hedging error. In reality, continuous rehedging is impossible and this raises the important practical question such as when should a portfolio manager rebalance the portfolio? In practice, many portfolio managers employ relatively simple deterministic rebalancing strategies, such as rebalancing at uniform time intervals, or rehedging when the underlying asset moves by a fixed number of ticks. While such strategies are easy to implement they will expose the portfolio to hedging risk, both in terms of timing and also as the strategies do not adequately consider market conditions. In this study we propose a rebalancing trigger based on the output from a GP-evolved hedging strategy that rebalances the portfolio based on dynamic nonlinear factors related to the condition of the market, derived from the theoretical literature, including a number of liquidity and volatility factors. The developed GP-evolved hedging strategy outperforms the deterministic time based hedging methods when tested on FTSE 100 call options. This paper represents the first such application of GP for this important application.

A comparative study of the canonical genetic algorithm and a real‐valued quantum‐inspired evolutionary algorithm

Purpose – Following earlier claims that quantum‐inspired evolutionary algorithm (QIEA) may offer advantages in high‐dimensional environments, the purpose of this paper is to test a real‐valued QIEA on a series of benchmark functions of varying dimensionality in order to examine its scalability within both static and dynamic environments.Design/methodology/approach – This paper compares the performance of both the QIEA and the canonical genetic algorithm (GA) on a series of test benchmark functions.Findings – The results show that the QIEA obtains highly competitive results when benchmarked against the GA within static environments, while substantially outperforming both binary and real‐valued representation of the GA in terms of running time. Within dynamic environments, the QIEA outperforms GA in terms of stability and run time.Originality/value – This paper suggests that QIEA has utility for real‐world high‐dimensional problems, particularly within dynamic environments, such as that found in real‐time f...

Benchmarking the performance of the real-valued Quantum-inspired Evolutionary Algorithm

Following earlier claims that Quantum-inspired Evolutionary Algorithm (QIEA) may offer advantages in high dimensional environments, this paper tests a real-valued QIEA on a series of benchmark functions of varying dimensionality in order to examine its scalability. The results are compared with those from a genetic algorithm using both a binary and real-valued representation. The results show that the QIEA obtains highly competitive results versus the genetic algorithm, while substantially outperforming both versions of the Genetic Algorithm (GA) in terms of running time. This suggests that QIEA may have substantial utility for real-world high dimensional problems.