### Browsing by Department "African Institute of Financial Markets and Risk Management"

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- ItemOpen AccessA decentralised asset registry to expand access to finance for the agricultural sector in South Africa(2019) Mzuku, Kungela; Georg, Co-PierreOver 61 percent of Africans are involved in agriculture; of this, only a few have access to financial services catered for their business. To get financial assistance, farmers have to provide sufficient collateral in the form of land, machinery and other large assets, many of which they do not own. Instead, farmers own mostly agricultural assets such as cattle, pigs and crop trees. The aim of this study is to make use of the agricultural resources available to farmers as collateral for financial loans. This was achieved through the development of a decentralised agricultural registry between farmers and the financial sector. Through an exploratory study, it was found many African countries introduced Movable Property laws to help increase acceptable collateral for financial loans. Unfortunately, many limitations were encountered which resulted in the adoption of the laws to be extremely low. As a result, this paper looks to blockchain technology as a solution as it would allow for transparency between farmers, government and financial sector. By creating a decentralised agricultural registry, farmers can register their biological assets and financiers can verify that the assets exists, are healthy and are currently not being used as collateral in another loan agreement. It is hoped that the registry can be used as a tool when financial agreements between farmers and banks are conducted.
- ItemOpen AccessA Feasibility Study on Using the Blockchain to Build a Credit Register for Individuals Who Do Not Have Access to Traditional Credit Scores(2019) Ortlepp, Bryony; Georg, Co-PierreIn South Africa and many other countries, credit registers and credit scores are used to determine how much credit a person can get access to, as well as the interest rate which they will be charged. In addition to this, some companies (such as insurance companies and rental agencies), use this data as part of the process to vet potential clients before allowing them to sign a contract. Part of the problem with this approach is that only certain records are stored on these credit registers. This excludes a large number of individuals, specifically those who are unbanked, those who have not got access to credit from formal institutions or those who do not own property and therefore pay their landlord for utilities. The purpose of this research is to determine the feasibility of using blockchain to store payment histories from small businesses to give their clients access to a credit record. The case study for this research will look specifically at a business which offers insurance to individuals living in informal settlements. This could be extended to many other businesses who work within informal settlements which allow cash payments on a regular basis for services offered. Shops in informal marketplaces which allow people to take products on credit and only pay later could also be included. By storing these transactions on the blockchain, individuals who would not usually have access to a credit history will have access to records of transactions that they have made and will be able to use these to show their ability and willingness to meet their financial obligations. This paper provides insight into existing credit registers and the process followed to build an informal credit register on the blockchain. The research covers an investigation into the feasibility of the project and it was found that this could is feasible and could add a lot of value, especially to those who do not have a credit history. There are many considerations, such as speed, security and costs which need to be taken into account, but these are outweighed by the benefits of the blockchain.
- ItemOpen AccessA Machine Learning Approach to Predicting the Employability of a Graduate(2019) Modibane, Masego; Georg, Co-PierreFor many credit-offering institutions, such as banks and retailers, credit scores play an important role in the decision-making process of credit applications. It becomes difficult to source the traditional information required to calculate these scores for applicants that do not have a credit history, such as recently graduated students. Thus, alternative credit scoring models are sought after to generate a score for these applicants. The aim for the dissertation is to build a machine learning classification model that can predict a students likelihood to become employed, based on their student data (for example, their GPA, degree/s held etc). The resulting model should be a feature that these institutions should use in their decision to approve a credit application from a recently graduated student.
- ItemOpen AccessA review of current Rough Volatility Methods(2021) Beelders, Noah; Soane, AndrewRecent literature has provided empirical evidence showing that the behaviour of volatility in financial markets is rough. Given the complicated nature of rough dynamics, a review of these methods is presented with the intention of ensuring tractability for those wishing to implement these techniques. The models of rough dynamics are built upon the fractional Brownian Motion and its associated powerlaw kernel. One such model is called the Rough Heston, an extension of the Classical Heston model, and is the main model of focus for this dissertation. To implement the Rough Heston, fractional Riccati ordinary differential equations (ODEs) must be solved; and this requires numerical methods. Three such methods in order of increasing complexity are considered. Using the fractional Adam's numerical method, the Rough Heston model can be effected to produce realistic volatility smiles comparable to that of market data. Lastly, a quick and easy approximation of the Rough Heston model, called the Poor Man's Heston, is discussed and implemented.
- ItemOpen AccessA Review of Multilevel Monte Carlo Methods(2020) Jain, Rohin; McWalter, ThomasThe Monte Carlo method (MC) is a common numerical technique used to approximate an expectation that does not have an analytical solution. For certain problems, MC can be inefficient. Many techniques exist to improve the efficiency of MC methods. The Multilevel Monte Carlo (ML) technique developed Giles (2008) is one such method. It relies on approximating the payoff at different levels of accuracy and using a telescoping sum of these approximations to compute the ML estimator. This dissertation summarises the ML technique and its implementation. To start with, the framework is applied to a European call option. Results show that the efficiency of the method is up to 13 times faster than crude MC. Then an American put option is priced within the ML framework using two pricing methods. The Least Squares Monte Carlo method (LSM) estimates an optimal exercise strategy at finitely many instances, and consequently a lower bound price for the option. The dual method finds an optimal martingale, and consequently an upper bound for the price. Although the pricing results are quite close to the corresponding crude MC method, the efficiency produces mixed results. The LSM method performs poorly within an ML framework, while the dual approach is enhanced.
- ItemOpen AccessAccounting for roll-over risk in the pricing of caps and floors(2022) Vidima, Sizwe; Backwell, AlexThe peak of the global financial crisis necessitated practitioners to rethink the single curve approach to pricing interest-rate derivatives. This was as a result of a violation in spot-forward parity relationships thereby prompting markets to realise the presence of a new type of risk and subsequently the need for a multi-curve pricing framework. The roll-over risk framework is one that accounts for liquidity constraints and default risk thereby providing a cogent explanation for the spotforward parity violation that led to the need for multiple curves. The primary objective of this work is to price XIBOR-based caps and floors under a framework which accounts for roll-over risk. This reformulation of interest-rate derivatives is achieved using Fourier Transform methods as well as Monte Carlo simulations for comparison. We found that the results obtained using the two approaches were comparable even though the two methods are different in nature. This agreement in prices is compelling evidence that the computations are correct.
- ItemOpen AccessAI/Machine learning approach to identifying potential statistical arbitrage opportunities with FX and Bitcoin Markets(2019) Ntsaluba, Kuselo Ntsika; Georg, Co-PierreIn this study, a methodology is presented where a hybrid system combining an evolutionary algorithm with artificial neural networks (ANNs) is designed to make weekly directional change forecasts on the USD by inferring a prediction using closing spot rates of three currency pairs: EUR/USD, GBP/USD and CHF/USD. The forecasts made by the genetically trained ANN are compared to those made by a new variation of the simple moving average (MA) trading strategy, tailored to the methodology, as well as a random model. The same process is then repeated for the three major cryptocurrencies namely: BTC/USD, ETH/USD and XRP/USD. The overall prediction accuracy, uptrend and downtrend prediction accuracy is analyzed for all three methods within the fiat currency as well as the cryptocurrency contexts. The best models are then evaluated in terms of their ability to convert predictive accuracy to a profitable investment given an initial investment. The best model was found to be the hybrid model on the basis of overall prediction accuracy and accrued returns.
- ItemOpen AccessAnalytical Solution of the Characteristic Function in the Trolle-Schwartz Model(2019) Van Gysen, Richard John; McWalter, Thomas; Kienitz, JoergIn 2009, Trolle and Schwartz (2008) produced an instantaneous forward interest rate model with several stylised facts such as stochastic volatility. They derived pricing formulae in order to price bonds and bond options, which can be altered to price interest rate options such as caplets, caps and swaptions. These formulae involve implementing numerical methods for solving an ordinary differential equation (ODE). Schumann (2016) confirmed the accuracy of the pricing formulae in the Trolle and Schwartz (2008) model using Monte-Carlo simulation. Both authors used a numerical ODE solver to estimate the ODE. In this dissertation, a closed-form solution for this ODE is presented. Two solutions were found. However, these solutions rely on a simplification of the instantaneous volatility function originally proposed in the Trolle and Schwartz (2008) model. This case happens to be the stochastic volatility version of the Hull and White (1990) model. The two solutions are compared to an ODE solver for one stochastic volatility term and then extended to three stochastic volatility terms.
- ItemOpen AccessApplication of Adjoint Differentiation (AD) for Calculating Libor Market Model Sensitivities(2018) Morley, Niall; McWalter, TomThis dissertation explores a key challenge of the financial industry â€” the efficient computation of sensitivities of financial instruments. The adjoint approach to solving affine recursion problems (ARPs) is presented as a solution to this challenge. A Monte Carlo setting is adopted and it is illustrated how computational efficiency in sensitivity calculation may be significantly improved via the pathwise derivatives method through adapting an adjoint approach. This is achieved through the reversal of the order of differentiation in the pathwise derivatives algorithm in comparison to the standard, intuitive â€˜forwardâ€™ approach. The Libor market model (LMM) framework is selected for examples to demonstrate these computational savings, with varying degrees of complexity of the LMM explored, from a one-factor model with constant volatility to a full factor model with time homogeneous volatilities.
- ItemOpen AccessApplication of Volatility Targeting Strategies within a Black-Scholes Framework(2019) Vakaloudis, Dmitri; Mahomed, ObeidThe traditional Black-Scholes (BS) model relies heavily on the assumption that underlying returns are normally distributed. In reality however there is a large amount of evidence to suggest that this assumption is weak and that actual return distributions are non-Gaussian. This dissertation looks at algorithmically generating a Volatility Targeting Strategy (VTS) which can be used as an underlying asset. The rationale here is that since the VTS has a constant prespecified level of volatility, its returns should be normally distributed, thus tending closer to an underlying that adheres to the assumptions of BS.
- ItemOpen AccessApplications of Gaussian Process Regression to the Pricing and Hedging of Exotic Derivatives(2021) Muchabaiwa, Tinotenda Munashe; Ouwehand, PeterTraditional option pricing methods like Monte Carlo simulation can be time consuming when pricing and hedging exotic options under stochastic volatility models like the Heston model. The purpose of this research is to apply the Gaussian Process Regression (GPR) method to the pricing and hedging of exotic options under the Black-Scholes and Heston model. GPR is a supervised machine learning technique which makes use of a training set to train an algorithm so that it makes predictions. The training set is composed of the input vector X which is a n Ã— p matrix and Y an nÃ—1 vector of targets, where n is the number of training input vectors and p is the number of inputs. Using a GPR with a squared-exponential kernel tuned by maximising the log-likelihood, we established that this GPR works reasonably for pricing Barrier options and Asian options under the Heston model. As compared to the traditional method of Monte Carlo simulation, GPR technique is 2 000 times faster when pricing barrier option portfolios of 100 assets and 1 000 times faster computing a portfolio of Asian options. However, the squared-exponential GPR does not compute reliable hedging ratios under Heston model, the delta is reasonably accurate, but the vega is off.
- ItemOpen AccessApproximating the Heston-Hull-White Model(2019) Patel, Riaz; Rudd, RalphThe hybrid Heston-Hull-White (HHW) model combines the Heston (1993) stochastic volatility and Hull and White (1990) short rate models. Compared to stochastic volatility models, hybrid models improve upon the pricing and hedging of longdated options and equity-interest rate hybrid claims. When the Heston and HullWhite components are uncorrelated, an exact characteristic function for the HHW model can be derived. In contrast, when the components are correlated, the more useful case for the pricing of hybrid claims, an exact characteristic function cannot be obtained. Grzelak and Oosterlee (2011) developed two approximations for this correlated case, such that the characteristics functions are available. Within this dissertation, the approximations, referred to as the determinist and stochastic approximations, were implemented to price vanilla options. This involved extending the Carr and Madan (1999) method to a stochastic interest rate setting. The approximations were then assessed for accuracy and efficiency. In determining an appropriate benchmark for assessing the accuracy of the approximations, the full truncation Milstein and Quadratic Exponential (QE) schemes, which are popular Monte Carlo discretisation schemes for the Heston model, were extended to the HHW model. These schemes were then compared against the characteristic function for the uncorrelated case, and the QE scheme was found to be more accurate than the Milstein-based scheme. With the differences in performance becoming increasingly noticeable when the Feller (1951) condition was not satisfied and the maturity and volatility of the Hull-White model (âŒ˜) was large. In assessing the accuracy of the approximations against the QE scheme, both approximations were similarly accurate when âŒ˜ was small. In contrast, when âŒ˜ was large, the stochastic approximation was more accurate than the deterministic approximation. However, the deterministic approximation was significantly faster than the stochastic approximation and the stochastic approximation displayed signs of potential instability. When âŒ˜ is small, the deterministic approximation is therefore recommended for use in applications such as calibration. With its shortcomings, the stochastic approximation could not be recommended. However, it did show promising signs of accuracy that warrants further investigation into its efficiency and stability.
- ItemOpen AccessBias-Free Joint Simulation of Multi-Factor Short Rate Models and Discount Factor(2018) Lopes, Marcio Ferrao; McWalter,Tom; Kienitz, JorgThis dissertation explores the use of single- and multi-factor Gaussian short rate models for the valuation of interest rate sensitive European options. Specifically, the focus is on deriving the joint distribution of the short rate and the discount factor, so that an exact and unbiased simulation scheme can be derived for risk-neutral valuation. We see that the derivation of the joint distribution remains tractable when working with the class of Gaussian short rate models. The dissertation compares three joint and exact simulation schemes for the short rate and the discount factor in the single-factor case; and two schemes in the multifactor case. We price European floor options and European swaptions using a twofactor Gaussian short rate model and explore the use of variance reduction techniques. We compare the exact and unbiased schemes to other solutions available in the literature: simulating the short rate under the forward measure and approximating the discount factor using quadrature.
- ItemOpen AccessBid-Ask Spread Modelling in the South African Bond Market(2018) Shaw, Matthew; Mohamed, Obeid; Taylor, DavidPitsillis and Taylor (2014) calculate bid-ask spread estimates of South African government bonds over a single year, using the models of De Jong and Rindi (2009) and Huang and Stoll (1997). This dissertation tests the effectiveness of both models by comparing the modelled equity spread estimates against the actual equity spread estimates. Furthermore, this dissertation investigates the stability of the De Jong and Rindi (2009) and Huang and Stoll (1997) models in the bond market by extending the spread estimate dataset to run annually over 5 years. The final section of this dissertation proposes a new method of estimating the bond spread through the use of a Kalman filter, as it can be used to leverage information from an onscreen market (albeit a different market) to imply bid-ask spread estimates in an off-screen market. The results indicate that the Huang and Stoll (1997) model consistently outperforms the De Jong and Rindi (2009) model. Furthermore, the yield estimate results of Pitsillis and Taylor (2014) align with the results obtained in this dissertation. The spread estimate results are stable over the 5-year period, indicating a strong provision of liquidity by the Primary Dealers.
- ItemOpen AccessBreak-Even Volatility(2019) Mitoulis, Nicolas; Taylor, David; Mahomed, ObeidA profit or loss (P&L) of a dynamically hedged option depends on the implied volatility used to price the option and implement the hedges. Break-even volatility is a method of solving for the volatility which yields no profit or loss based on replicating the hedging procedure of an option on a historical share price time series. This dissertation investigates the traditional break-even volatility method on simulated data, how the break-even formula is derived and details the implementation with reference to MATLAB. We extend the methodology to the Heston model by changing the reference model in the hedging process. Resultantly, the need to employ characteristic function pricing methods arises to calculate the Heston model sensitivities. The break-even volatility solution is then found by means of an optimisation of the continuously delta hedged P&L over the Heston model parameters.
- ItemOpen AccessBreak-even volatility for caps, floors and swaptions(2019) Cresswell, Wade; Mahomed, ObeidThis dissertation investigates break-even volatility in the context of the South African interest rate market. Introduced by Dupire (2006), break-even volatility is a retrospective measure defined as the volatility that ensures the profit or loss from a delta hedged option position is zero. Break-even volatility sheds light on the inner structure of the market and is a promising investigatory tool. Insurance houses in South Africa are interested in modelling long-dated interest rate derivatives embedded within their liabilities. In pursuit of this goal, some are currently calibrating the Lognormal Forward-LIBOR Market Model to market prices. They rarely directly trade in said derivatives, but merely delta hedge their risk daily. In this case, break-even volatility surfaces become more relevant than recovering market prices (which incorporate the banks risk premium and profit margin) as it should better represent the historical cost of replicating the option under consideration. This dissertation ultimately assesses the use of the Lognormal Forward-LIBOR Market Model in the South African interest rate market using break-even volatility. It is found that several caps and swaptions are trading at volatilities that differ significantly from their break-even volatility estimates. Furthermore, through an investigation into the calibration of the Lognormal Forward-LIBOR Market Model to break-even volatilities, an argument that the underlying dynamics of the model are incompatible with that of the South African interest rate market is developed.
- ItemOpen AccessCalibrating Term Structure Models to an Initial Yield Curve(2020) Sylvester, Matthew; Backwell, AlexThe modelling of the short rate offers many advantages, with the models explored in this dissertation all offering closed-form, analytic formulae for bond prices and for options on bonds. Often, a vital primary condition is for a model to be calibrated to the initial term structure and to recover the bond prices observed in the market â€“ that is, to be calibrated to the initial yield curve. Under the two exogenous models explored in this dissertation, the Hull-White and the CIR++, the effect of increasing the volatility parameter of the SDE increases the mean of the short rate. Increasing volatility of an SDE is a common approach to stress testing a model, as such, the consequences of bumping volatility in a calibrated model is a vital concern. The Hull-White model and CIR++ model were calibrated to market data, with the former being able to match the observed cap prices, while the latter failed, displaying an upper bound on cap prices. Investigating this, under CIR++ model, bond option prices are shown to not be straightforward increasing functions of the volatility parameter. In fact, for high volatility, bond option prices display an upper limit before decreasing, thus providing a limit to the level of cap prices too. This dissertation points to the reason residing in the underlying CIR model from which the CIR++ is based on, and the manner in which the model is extended
- ItemOpen AccessCharacteristic function pricing with the Heston-LIBOR hybrid model(2019) Sterley, Christopher; Ouwehand, Peter; McWalter, ThomasWe derive an approximate characteristic function for a simplified version of the Heston-LIBOR model, which assumes a constant instantaneous volatility structure in the underlying LIBOR market model. We also implement measures to improve the numerical stability of the characteristic function derived in this dissertation as well as the one derived by Grzelak and Oosterlee. The ultimate aim of the dissertation is to prevent these characteristic functions from exploding for given parameter values.
- ItemOpen AccessData Capture Automation in the South African Deeds Registry using Optical Character Recognition (OCR)(2019) Favish, Ashleigh; Georg, Co-PierreThe impact of apartheid on land registration is still evident within South Africa. The Deeds Registry is facing a current backlog in registering an estimated 900,000 title deeds. Providing formal ownership, through title, is seen as necessary for unlocking the 'dead capitalâ€™ of unregistered property, fostering access to capital markets and poverty alleviation. Within the current legislative framework, the Deeds Registry only accepts paper documents, which introduces inefficiencies. To increase the number of deeds processed per day, automation of manual data capture is tested using an OCR pipeline. To adapt to the linguistics used in title deeds, text analysis and parsing is done using Regex. Uploading the scanned title deeds onto IPFS is as an additional security measure included in the pipeline. Previous research has failed to apply these techniques to formal land registration or other South African government institutions. The preliminary results show that this pipeline has an overall accuracy of 89.6%. This represents the comparison of the expected output to the output extracted using OCR. The results are significantly less accurate when classifying handwritten and stamped information. Thus, further measures are required to increase accuracy for these fields. The OCR accuracy was 98.3% for the fields extracted from typed text characters. This is within the accuracy range of manual data capture. A secondary quality check, which is currently done on manual data capture, would still be necessary to ensure accuracy of inputs. Overall it appears that this application would be appropriate for incorporation into the Deeds Registry to streamline their processes while ensuring title deed validity.
- ItemOpen AccessDeep Calibration of Option Pricing Models(2022) Dadah, Sahil; Ouwehand, PeterThis dissertation investigates the calibration efficiency of short rate models using deep neural networks. The main focus is on the calibration of one-and-two factor Hull-White models to caplets and swaptions data, where the inputs are interest rate derivative prices or implied volatilities, and the outputs are the model parameters. A direct and indirect neural network calibration framework is adopted. The former method involves a direct inversion of the standard option pricing function using neural network. The indirect framework uses two consecutive steps; the first step estimates the option pricing function using a neural network. This is followed by applying the pre-trained model in a calibration procedure to fit the model parameters to a set of market observables. The neural networks are trained using simulated data and an optimum set of hyperparameters is obtained via the Bayesian optimization. The best set of hyperparameters is used to train the networks and tested on out-of-sample actual market yield curves data. It is shown that the direct method has substantial improvements in time with a sacrifice in accuracy (a mean relative error of 2.88%). On the other hand, using the indirect method, it is shown that the calibrated parameters reprice the set of options to a mean relative error of less than 0.1% (similar to numerical calibration), with a significant improvement in speed whose execution is twenty-six times faster compared to the conventional calibration procedures currently used.