Browsing by Author "Soane, Andrew"

Now showing 1 - 5 of 5
  • Thumbnail Image
    Item
    Open Access
    A review of current Rough Volatility Methods
    (2021) Beelders, Noah; Soane, Andrew
    Recent 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.
  • Thumbnail Image
    Item
    Open Access
    Calibrating the Hurst Parameter for Rough Volatility Models with Application in the South African Market
    (2022) Pettit, Paul; Soane, Andrew
    It is known that accurate and efficient calibration of any fractional stochastic volatility model is important for trading and risk management purposes. Under the rough Heston model proposed by El Euch et al. (2019), the Hurst parameter governs the roughness of the volatility process. This dissertation explores the different calibration methods used to obtain an estimate for the Hurst parameter, under the scope of the rough Heston model. Three different calibration methods are presented, namely, a Brute Force minimisation procedure, a Neural Network calibration and a Linear Regression procedure. European option prices are simulated from the rough Heston model using the characteristic function pricing approach as in El Euch and Rosenbaum (2019) and numerical techniques, such as the fractional Adams method which are implemented in MATLAB. These simulated prices are then used to test and compare the three proposed calibration methods in terms of accuracy and efficiency. Thereafter, additional experiments are conducted on South African market data from traded options and the fitted models are compared across the calibration methods used. The results of our numerical experiments are used to justify the nature of rough volatility in the South African options market and recommendations are made on the appropriateness of each calibration scheme in practice. Overall, we find that the performance measured by accuracy on our simulated data of the Neural Network method is similar to the Brute Force minimisation method, whereas the Linear Regression method, is the least accurate. When calibrating on the market data, the results of the fitted models show that both the Neural Network and Brute Force method resembles the market behaviour. All three methods were shown to be suitable in estimating the Hurst parameter and suggesting rough volatility in this South African market.
  • Thumbnail Image
    Item
    Open Access
    Latent State and Parameter Estimation of Stochastic Volatility/Jump Models via Particle Filtering
    (2018) Soane, Andrew
    Particle filtering in stochastic volatility/jump models has gained significant attention in the last decade, with many distinguished researchers adding their contributions to this new field. Golightly (2009), Carvalho et al. (2010), Johannes et al. (2009) and Aihara et al. (2008) all attempt to extend the work of Pitt and Shephard (1999) and Liu and Chen (1998) to adapt particle filtering to latent state and parameter estimation in stochastic volatility/jump models. This dissertation will review their extensions and compare their accuracy at filtering the Bates stochastic volatility model. Additionally, this dissertation will provide an overview of particle filtering and the various contributions over the last three decades. Finally, recommendations will be made as to how to improve the results of this paper and explore further research opportunities.
  • Thumbnail Image
    Item
    Open Access
    Parameter learning with particle filters
    (2020) Pather, Vegan; Rudd, Ralph; Soane, Andrew
    Common applications of asset-pricing models in practice rely on recalibrating model parameters periodically for effective risk management. Yet, these model parameters are often assumed to be constant over time, thereby countering the notion of readjusting these values. A possible solution to this problem is to recalibrate at times where observed market prices cannot realistically match model prices based on parameter values at those times. This dissertation aims to test the effectiveness of a possible algorithm which can be used in optimally identifying such times. An overview is provided of the recently proposed particle filter with accelerated adaptation which has demonstrated rapid time detection for changes in parameter values and has been applied to regime-shifting and stochastic volatility models. Numerical and graphical evidence of parameter and volatility estimation will be provided under regime-shifting parameters for the Heston (1993) stochastic volatility model. The filter demonstrates rapid adaptation in estimating parameter values and accurate estimation of the volatility process. Furthermore, we provide a discussion for possible extensions towards a metric for optimal recalibration times.
  • Thumbnail Image
    Item
    Open Access
    The Lifted Heston Stochastic Volatility Model
    (2020) Broodryk, Ryan; Backwell, Alex; Soane, Andrew
    Can we capture the explosive nature of volatility skew observed in the market, without resorting to non-Markovian models? We show that, in terms of skew, the Heston model cannot match the market at both long and short maturities simultaneously. We introduce Abi Jaber (2019)'s Lifted Heston model and explain how to price options with it using both the cosine method and standard Monte-Carlo techniques. This allows us to back out implied volatilities and compute skew for both models, confirming that the Lifted Heston nests the standard Heston model. We then produce and analyze the skew for Lifted Heston models with a varying number N of mean reverting terms, and give an empirical study into the time complexity of increasing N. We observe a weak increase in convergence speed in the cosine method for increased N, and comment on the number of factors to implement for practical use.