Now showing 1 - 7 of 7
- PublicationParameter uncertainty in Kalman filter estimation of the CIR term structure model(University College Dublin. School of Business. Centre for Financial Markets, 2007)The Cox, Ingersoll and Ross (1985) term structure model describes the stochastic evolution of government bond yield curves over time using a square root Orstein-Uhlenbeck diffusion process, whilst imposing cross-sectional no-arbitrage restrictions between yields of different maturities. A Kalman filter approach can be used to estimate the parameters of the CIR model from panel data consisting of a time series of bonds of different maturities. The parameters are estimated by optimising a quasi log-likelihood function that results from the prediction error decomposition of the Kalman filter. The quasi log-likelihood function is usually optimised with a deterministic gradient based optimisation technique such as a quadratic hill climbing optimiser. This paper uses an evolutionary optimiser known as differential evolution (DE) to optimise over the parameter space. The DE optimiser is more likely to find the global maximum than a deterministic optimiser in the presence of a non-convex objective function which may be the case in multifactor term structure models with non-negativity constraints and parameter constraints. The method is applied to estimate parameters from a one and two-factor Cox, Ingersoll and Ross (1985) model. It is shown that in the two factor model the problem of local maxima arises whereby a number of different parameter vectors perform equally well in the estimation procedure. Fixed income derivative prices are particular sensitive to term structure parameters such as the volatility, the rate of mean reversion, and the market price of risk of each factor. The effect of different optimal parameter vectors on fixed income derivatives is examined and is found to be significant.
- PublicationPath dependent option pricing under Lévy processes applied to Bermudan options(University College Dublin. School of Business. Centre for Financial Markets, 2004-12)A model is developed that can price path dependent options when the underlying process is an exponential Lévy process with closed form conditional characteristic function. The model is an extension of a recent quadrature option pricing model so that it can be applied with the use of Fourier and Fast Fourier transforms. Thus the model possesses nice features of both Fourier and quadrature option pricing techniques since it can be applied for a very general set of underlying Lévy processes and can handle exotic path dependent features. The model is applied to European and Bermudan options for geometric Brownian motion, a jump-diffusion process, a variance gamma process and a normal inverse Gaussian process. However it must be noted that the model can also price other path dependent exotic options such as lookback and Asian options.
- PublicationPricing European and American options under Heston's stochastic volatility model with accelerated explicit finite differencing methodsWe 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 Heston’s stochastic volatility model we demonstrate degrees of acceleration over standard explicit methods sufficient to achieve comparable, or superior, efficiencies to a benchmark implicit scheme. We conclude that STS is a powerful tool for the numerical pricing of options and propose them as the method-of-choice for exotic financial instruments in two and multi-factor models.
- PublicationMeasuring and Analyzing Liquidity and Volatility Dynamics in the Euro-Area Government Bond MarketThis chapter examines the impact the European sovereign debt market crisis had on liquidity and volatility dynamics and their interdependencies in the eurozone government bond market. In particular, we examine the impact across different countries and across different maturity buckets within individual countries. A comprehensive high-frequency dataset from MTS, Europe's premier electronic fixed-income trading market, is employed to construct a variety of microstructure liquidity and volatility measures. We analyze important trends in these measures over both tranquil and crisis periods. Additionally, we study time-varying correlations as well as the intertemporal interactions of liquidity proxies with volatility and returns. Our findings provide useful insights to regulators and policy makers on the relative strengths and weaknesses of domestic and global financial systems.
- PublicationA simple recursive numerical method for Bermudan option pricing under Lévy processes(University College Dublin. School of Business. Centre for Financial Markets, 2006-08)A numerical method is developed that can price options, including exotic options that can be priced recursively such as Bermudan options, when the underlying process is an exponential Lévy process with closed form conditional characteristic function. The numerical method is an extension of a recent quadrature option pricing method so that it can be applied with the use of fast Fourier transforms. Thus the method possesses desirable features of both transform and quadrature option pricing techniques since it can be applied for a very general set of underlying Lévy processes and can handle certain exotic features. To illustrate the method it is applied to European and Bermudan options for a log normal process, a jump diffusion process, a variance gamma process and a normal inverse Gaussian process.
- PublicationThe Variance Gamma Self-Decomposable Process in Actuarial ModellingA scaled self-decomposable stochastic process put forward by Carr, Geman, Madan and Yor (2007) is used to model long term equity returns and options prices. This parsimonious model is compared to a number of other one-dimensional continuous time stochastic processes (models) that are commonly used in finance and the actuarial sciences. The comparisons are conducted along three dimensions: the models ability to fit monthly time series data on a number of different equity indices; the models ability to fit the tails of the times series and the models ability to calibrate to index option prices across strike price and maturities. The last criteria is becoming increasingly important given the popularity of capital gauranteed products that contain long term imbedded options that can be (at least partially) hedged by purchasing short term index options and rolling them over or purchasing longer term index options. Thus we test if the models can reproduce a typical implied volatility surface seen in the market.
- PublicationOn the term structure of liquidity in the European sovereign bond marketThe paper provides a high-frequency analysis of liquidity dynamics in the eurozone sovereign bond market over tranquil and crisis periods. We study time series of liquidity across the yield curve using high-frequency data from MTS, one of Europe’s leading electronic fixed-income trading platforms. We document flight-to-liquidity effects as investors prefer to trade on shorter-term benchmarks during liquidity dry-ups. We provide evidence of significant commonalities in spread and depth liquidity proxies which are weaker during the crisis period for both core and periphery economies although periphery countries display higher commonality than core countries during the crisis. We show that illiquidity of the periphery countries plays an important role in market dynamics and Granger causes illiquidity, volatility, returns, and CDS spreads across the maturity spectrum in both calm and crisis periods. Liquidity is priced both as a characteristic and as a risk factor even when controlling for credit risk, pointing to liquidity’s systematic dimension and importance.
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