Lower hedging of American contingent claims with minimal surplus risk in finite-state financial markets by mixed-integer linear programming

Cataloged from PDF version of article.The lower hedging problem with a minimal expected surplus risk criterion in incomplete markets is studied for American claims in finite state financial markets. It is shown that the lower hedging problem with linear expected surplus criterion for American contingent claims in finite state markets gives rise to a non-convex bilinear programming formulation which admits an exact linearization. The resulting mixed-integer linear program can be readily processed by available software. (c) 2011 Elsevier B.V. All rights reserved

Tactical Assets Allocation: Evidence from the Nigerian Banking Industry

The core of portfolio selection theory centers on striking a balance between risk-return trade-off of a given investment layout so as to maximize benefits. Literature reveals that portfolio selection or asset allocation problems often involve the use of mathematical programming in propounding solution. This paper uses a blend of simultaneous equation and graphical approach to linear programming algorithm to help solve investors’ problem in allocating assets among various alternatives when faced with problems associated with risk-return trade-off

A stochastic programming model for dynamic portfolio management with financial derivatives

Stochastic optimization models have been extensively applied to financial portfolios and have proven their effectiveness in asset and asset-liability management. Occasionally, however, they have been applied to dynamic portfolio problems including not only assets traded in secondary markets but also derivative contracts such as options or futures with their dedicated payoff functions. Such extension allows the construction of asymmetric payoffs for hedging or speculative purposes but also leads to several mathematical issues. Derivatives-based nonlinear portfolios in a discrete multistage stochastic programming (MSP) framework can be potentially very beneficial to shape dynamically a portfolio return distribution and attain superior performance. In this article we present a portfolio model with equity options, which extends significantly previous efforts in this area, and analyse the potential of such extension from a modeling and methodological viewpoints. We consider an asset universe and model portfolio set-up including equity, bonds, money market, a volatility-based exchange-traded-fund (ETF) and over-the-counter (OTC) option contracts on the equity. Relying on this market structure we formulate and analyse, to the best of our knowledge, for the first time, a comprehensive set of optimal option strategies in a discrete framework, including canonical protective puts, covered calls and straddles, as well as more advanced combined strategies based on equity options and the volatility index. The problem formulation relies on a data-driven scenario generation method for asset returns and option prices consistent with arbitrage-free conditions and incomplete market assumptions. The joint inclusion of option contracts and the VIX as asset class in a dynamic portfolio problem extends previous efforts in the domain of volatility-driven optimal policies. By introducing an optimal trade-off problem based on expected wealth and Conditional Value-at-Risk (CVaR), we formulate the problem as a stochastic linear program and present an extended set of numerical results across different market phases, to discuss the interplay among asset classes and options, relevant to financial engineers and fund managers. We find that options’ portfolios and trading in options strengthen an effective tail risk control, and help shaping portfolios returns’ distributions, consistently with an investor's risk attitude. Furthermore the introduction of a volatility index in the asset universe, jointly with equity options, leads to superior risk-adjusted returns, both in- and out-of-sample, as shown in the final case-study

The Mathematics and Statistics of Quantitative Risk Management

It was the aim of this workshop to gather a multidisciplinary and international group of scientists at the forefront of research in areas related to the mathematics and statistics of quantitative risk management. The main objectives of this workshop were to break down disciplinary barriers that often limit collaborative research in quantitative risk management, and to communicate the state of the art research from the different disciplines, and to point towards new directions of research

A study in the financial valuation of a topping oil refinery

Oil refineries underpin modern day economics, finance and engineering – without their refined products the world would stand still, as vehicles would not have petrol, planes grounded without kerosene and homes not heated, without heating oil. In this thesis I study the refinery as a financial asset; it is not too dissimilar to a chemical plant, in this respect. There are a number of reasons for this research; over recent years there have been legal disputes based on a refiner's value, investors and entrepreneurs are interested in purchasing refineries, and finally the research in this arena is sparse. In this thesis I utilise knowledge and techniques within finance, optimisation, stochastic mathematics and commodities to build programs that obtain a financial value for an oil refinery. In chapter one I introduce the background of crude oil and the significance of the refinery in the oil value chain. In chapter two I construct a traditional discounted cash flow valuation often applied within practical finance. In chapter three I program an extensive piecewise non linear optimisation solution on the entire state space, leveraging off a simulation of the refined products using a set of single factor Schwartz (1997) stochastic equations often applied to commodities. In chapter four I program an optimisation using an approximation on crack spread option data with the aim of lowering the duration of solution found in chapter three; this is achieved by utilising a two-factor Hull & White sub-trinomial tree based numerical scheme; see Hull & White (1994) articles I & II for a thorough description. I obtain realistic and accurate numbers for a topping oil refinery using financial market contracts and other real data for the Vadinar refinery based in Gujurat India

Innovations in Quantitative Risk Management

Quantitative Finance; Game Theory, Economics, Social and Behav. Sciences; Finance/Investment/Banking; Actuarial Science

Innovations in Quantitative Risk Management

Quantitative Finance; Game Theory, Economics, Social and Behav. Sciences; Finance/Investment/Banking; Actuarial Science

Tax effects on investments

This doctoral thesis investigates empirically and theoretically the effect of tax on the composition of the optimal allocation of wealth to risky assets from various points of view. The first empirical chapter considers the effect of tax on a U.K. personal investor targeting domestic financial products. This research helps investors estimate the impact of a future tax change and maximize their portfolio return using a newly proposed optimization model and solution method. Following Bonami and Lejeune (2009), personal portfolios are constrained to meet or exceed a prescribed return threshold with a high confidence level and satisfy buy-in threshold and diversification constraints. Their model is improved by incorporating complex tax trading rules with withdrawal features that enhance those considered by Osorio et al. (2004, 2008). A solution based on Greedy methods is developed to deal with the proposed large-scale portfolio optimization problem. The empirical results report substantial non-linear tax effects on riskier assets and enhanced effects of withdrawal tax only when tax rates are high. The developed framework better enables investors to react to tax changes, and tax policy makers to quantify the influence of tax changes on private investment preferences. The second empirical chapter investigates the effect of an international transaction tax, the so-called ‘Tobin tax’, from the point of view of U.K., U.S., and E.U. personal investors targeting international financial products. This empirical research helps the policy maker to estimate the impact of Tobin tax on international capital flows and, therefore, assess the optimal way to introduce the new tax. An optimization model is proposed to maximize the expected net Sharpe ratio and find the optimal risky portfolio internationally. Complex trading and tax rules are considered. To examine the precise effects of different investment and transaction tax rules, a comparison of four tax settings is presented: source only, residence only, mixed with credit and mixed with double taxation. The experimental results show that a source only tax union has more capital transits in international markets than a residence only tax union, and its optimal market portfolio is more sensitive to regional tax policy. In a mixed tax system, double taxation between residence- and source-taxed markets significantly reduces the attraction of the latter while its attraction is maintained with the credit method. Tobin tax can reduce the volatility of the market but the effect varies with tax rate, certain market specifications (e.g., expected returns and correlations with overseas markets) and investment tax rules. It does not depend on which side of the capital flow (inflow or outflow) is subject to Tobin tax. Finally, an agreement among countries to produce a consistent Tobin tax rate globally can significantly reduce the negative effect of Tobin tax on capital flows while retaining its positive effect on market stability in comparison to heterogeneous Tobin tax rates. Finally, the third analytical chapter investigates theoretically the effect of tax from the point of view of an arbitrageur. This theoretical research addresses the condition of the existence of arbitrage opportunities on an after-tax basis, helping the policy maker improve the fairness and efficiency of markets by addressing effective tax policy. To track tax arbitrage, continuous time optimization models are developed with heterogeneous taxation between investors programmed with continuous rather than static income and capital gains (or losses). It is proved analytically that arbitrage opportunities exist for both perfectly correlated and non-perfectly correlated assets. For perfectly correlated assets, the analysis shows that tax arbitrage may exist, with the investor’s top tax rate and some static asset parameters determining the existence of arbitrage opportunities. It is also proved that many of the equilibria obtained under income tax only are not optimal if investors are also subject to capital gains tax. For non-perfectly correlated assets, however, it is the market prices of cap and floor options on asset returns that decide the existence of tax arbitrage. In the government fixed income bond market, tax arbitrage between investors is difficult to eliminate unless investors are all subject to the same tax rates. But the return from this arbitrage can be limited if the government applies the same top tax rate to all investors