Browsing by Author "Ware, Antony F."

Now showing 1 - 10 of 10
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    Adaptive wavelet collacation methods for option pricing PDEs
    (2006) Li, Hua; Ware, Antony F.
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    An adaptive local scaling function representation
    (2006) Quaife, Bryan; Ware, Antony F.
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    Hedging Canadian oil: an application of currency translated options
    (2010) Kitchen, Cliff; Ware, Antony F.
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    Improved Downward Wavefield with Applications to Reverse Time Migration
    (2016-01-29) Alnabulsi, Salam; Rios, Cristian; Breverman, Elena; Morin, Pedro; Krebes, Edward S.; Margrave, Gary F.; Ware, Antony F.
    In this research, we introduce a new technique for wave propagation which produces a lesser amount of reflections in the resulting wavefield. Using these wave-fields in the Reverse Time Migration scheme aims to decrease the negative effect of the multiples that occur in the imaging process. Based on the technique stemming from the absorbing boundary conditions, we implement these conditions inside the domain to generate a forward wavefield while minimizing reflections when going through horizontal interfaces. We test two types of velocity models: elastic and viscoelastic. The benefit of using the viscoelastic model is that it takes into account the attenuation incurred by fluid fill in porous media and, hence, model the effect of amplitude reduction in the imaging process. The finite difference method was used to generate the compressional wavefield in the elastic model, while the finite element method was used for the viscoelastic model. The images were generated using the cross-correlation and the normalized imaging conditions. Finally, we test the approximated velocity models in order to mimic real-field applications. The application of reverse time migration, under this new technique not only detects interface locations, but also creates structural images, and it can identify different types of the saturated fluid in porous media.
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    Nonequispaced fourier transform for option pricing
    (2008) Xu, Li; Ware, Antony F.
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    Optimal valuation of natural gas storage
    (2012) Ogunsolu, Mobolaji Olutomi; Ware, Antony F.
    This thesis focuses on the valuation of natural gas storage. We investigate the peculiar behavior of gas prices including the distribution of log returns, mean reversion and sea­sonality. We then model natural gas spot prices as a two-factor stochastic differential equation with mean reversion and seasonality properly accounted for in the model. These characteristics are common to commodities ( electricity, gas, agricultural products), un­like other financial assets (for example stocks, bonds etc.) whose availability and usage are not seasonal in nature and whose prices do not tend to revert back to an average long term mean. In addition, we also exploit the relationship between spot prices and futures prices to model and calibrate natural gas price spot and futures prices. Using the two-factor gas price model, we model the value of a gas storage as a stochastic control problem [8]. The timing optionality of the gas storage problem makes it similar to a constrained American option on the inter-temporal spread of gas prices. This problem can be solved by extending the Least Squares Monte Carlo (LSM) approach of Longstaff and Schwartz (2001) for pricing early exercise options [20].
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    Portfolio optimization under downside risk measures
    (2004) Dmitrasinovic-Vidovic, Gordana; Ware, Antony F.
    Portfolio optimization with respect to a risk measure that is coherent, easy to evaluate on large portfolios, and only penalizes low returns is of great value to practitioners and academics. In this thesis we consider risk measures defined by a-quantiles, and risk measures defined by tail means. We call these measures downside risk measures. We derive analytic expressions for all these risk measures, and investigate their characteristics. The particular quantile based risk measures we consider are: value at risk (VaR) , which is defined as the difference between the expected wealth and the corresponding a-quantile, capital at risk (GaR), defined as the difference between the wealth invested into the bond and the corresponding a-quantile, and relative value at risk (RVaR) , which is the ratio of the value at risk to the expected wealth. The tail mean based risk measures we investigate are: conditional value at risk (GVaR), defined as the difference between the riskless wealth and the tail mean, conditional capital at risk (GGaR) , defined as the difference between the expected wealth and the tail mean, and relative conditional value at risk (RGVaR) , which is the ratio of the conditional value at risk to the expected wealth. We show that only GGaR is a coherent risk measure, while GVaR and RGVaR are subadditive. The quantile based risk measures VaR, GaR and RVAR are not subadditive in general, so that none of these measures is coherent. We investigate continuous time portfolio selection problems under downside risk measures GaR, GGaR, VaR, RVaR, GVaR and RGVaR, in the Black Scholes setting, with time dependent parameters and deterministic, time dependent portfolios. Based on an idea introduced by Emmer at al., we introduce the fundamental dimension reduction procedure which transforms m-dimensional optimization problems into one-dimensional optimization problems. This idea leads to an optimal strategy which is a weighted average of the bond and Merton's portfolio, where the weights depend on the choice of the risk measure and the investor's risk tolerance. This result is an illustration of the two-fund separation theorem. The optimization results under GGaR and GaR favor investing into stocks over a longer time horizon, which is consistent with the common knowledge that stocks in the long run tend to outperform bonds. Under RVaR and RGVaR the portion of the wealth invested into the risky assets depends only on the investor's risk tolerance, regardless of the initial investment or the market setting. The optimization results under VaR and GVaR are counterintuitive in the sense that in better markets and during longer time horizons, we tend to invest less into the risky assets under these risk measures. We also investigate constrained portfolio selection problems where short-selling is not allowed, and optimization problems where the optimal solution is a constant portfolio. Finally, we provide several numerical examples which illustrate how the time dependency of the parameters can model the business cycle or the periodicity in the stocks' dynamics.
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    Stochastic models for gas prices
    (2004) Xu, Zhiyong; Ware, Antony F.
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    VIX-linked GMMB under affine GARCH models and its Diffusion Limits
    (2018-07-06) Chen, Yuyu; Badescu, Alexandru M.; Ware, Antony F.; Swishchuk, Anatoliy V.
    In variable annuity (VA) industry, to compensate for the liability coming from embedded riders in VA, insurer usually charge a fixed percentage of investment fund as the riders fee. However, the traditional fixed-fee structure would misalign insurer’s income and liability and in consequence cause risk management challenges for insurer. In 2013, the Chicago Board of Options Exchange (CBOE) suggests linking riders fee in variable annuity with VIX index in a white paper and shows that VIX-linked fee structure can help to re-align insurer’s income and liability using non-parametric models. Affine GARCH models are used in this work to analyze VIX-linked fee structure for VA with guarantee minimum maturity benefit (GMMB). A closed-form solution to GMMB has been derived and is used to determine a fair fee structure. Comparison between fixed-fee structure and VIX-linked fee structure has been been shown by numerical examples.