First Singapore Conference on Quantitative Finance
(23 Feb 2009)

Jointly organized with Saw Centre for Financial Studies

~ Abstracts ~


Tractable Robust Expected Utility and Risk Models for Portfolio Optimization
Melvyn Sim, Department of Decision Sciences, National University of Singapore

Expected utility models in portfolio optimization are based on the assumption of complete knowledge of the distribution of random returns. In this paper, we relax this assumption to the knowledge of only the mean, covariance and support information. No additional restrictions on the type of distribution such as normality is made. The investor's utility is modeled as a piecewise-linear concave function. We derive exact and approximate optimal trading strategies for a robust (maximin) expected utility model, where the investor maximizes his worst-case expected utility over a set of ambiguous distributions. The optimal portfolios are identified using a tractable conic programming approach. Extensions of the model to capture asymmetry using partitioned statistics information and box-type uncertainty in the mean and covariance matrix are provided. Using the optimized certainty equivalent framework, we provide connections of our results with robust or ambiguous convex risk measures, in which the investor minimizes his worst-case risk under distributional ambiguity. New closed form results for the worst-case OCE risk measures and optimal portfolios are provided for two and three-piece utility functions. For more complicated utility functions, computational experiments indicate that such robust approaches can provide good trading strategies in financial markets.

This is joint work with Karthik Natarajan and Joline Uichanco.

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Illiquidity, Portfolio Constraints, and Diversification
Min Dai, Department of Mathematics, National University of Singapore

We consider a fund that can trade a liquid stock and an illiquid stock that is subject to proportional transaction costs. The percentage of capital allocated to the illiquid stock is restricted to remain between a lower bound and an upper bound. We characterize the optimal trading strategy for the illiquid stock which is determined by the optimal buy boundary and the optimal sell boundary between which no transaction occurs.

We also conduct an extensive numerical analysis on trading strategies, liquidity premium, and diversification. Constantinides (1986) concludes that transaction costs only have a second-order effect on liquidity premia. We find that the presence of portfolio constraints can significantly magnify the effect of transaction costs on liquidity premium and can make it more than a first-order effect. Correlation coefficient between the two stocks affects the efficiency of diversification and thus can significantly alter the optimal trading strategy in both stocks.

This work is joint with Hanqing Jin and Hong Liu.

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Co-Integration in Crude Oil Components and the Pricing of Crack Spread Options
Jin-Chuan Duan, Cycle and Carriage Professor of Finance, Director, Risk Management Institute, National University of Singapore

The crack spread options traded at the New York Mercantile Exchange are American-style futures spread options on the one-to-one volume-adjusted difference between the futures price of a refined petroleum product and that of light sweet crude oil. We investigate the importance of co-integration and maturity effects in pricing the two most common of these options, namely
Heating Oil/Crude and Gasoline/Crude spread options. We compare the performance of five models: a bivariate constant-volatility model, a bivariate GARCH model with and without maturity effects, and the same two GARCH models being augmented with co-integration. The model parameters are estimated using futures prices, and the theoretical option prices are computed using a primal simulation technique. The evidence for co-integration, stochastic volatility and maturity effects is strong in the futures prices. The option prices also show support for these data features.

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Market Design for Emission Trading Schemes
Hinz Juri, Department of Mathematics, National University of Singapore

Emission trading schemes, also known as cap and trade systems, have been designed to reduce pollution by introducing appropriate market mechanisms. In such systems, a central authority sets a limit (cap) on the total amount of pollutant that can be emitted within a pre-determined period. To ensure that this target is complied with, a certain number of credits are allocated to appropriate installations, and a penalty is applied as a charge per unit of pollutant emitted outside the limits of a given period.
This regulatory framework introduces a market for emission allowances and for appropriate emission-related financial instruments. In this talk, we give an analysis of emission trading schemes and quantitatively investigate the impact of emission regulation on consumers costs and company?s profits. Moreover, we address logical principles underlying fair valuation of emission-related financial products.

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On The Term Structure of Model-free Volatilities and Volatility Risk Premium
Kian Guan Lim, Lee Kong Chian School of Business, Singapore Management University

We present a method to compute model-free volatility more accurately than existing methods, which allows for the construction of a term structure of model-free volatilities up to 450-day constant maturity. Properties of the volatility term structure and volatility risk premium are studied using S&P 100 index options

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Singular Stochastic Control Problems in Investment Theory
Tiong Wee Lim, Department of Statistics and Applied Probability, National University of Singapore

A certain class of singular stochastic control problems can be shown to be "equivalent" to optimal stopping. The problem of reversible investment belongs to this class of problems and can be solved by a relatively computationally inexpensive backward induction algorithm. We show how to extend this algorithm to solve a class of singular stochastic control problems which are not exactly equivalent to optimal stopping and provide an illustration using the problem of option hedging in the presence of transaction costs.

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Using High-Frequency Transaction Data to Estimate the Probability of Informed Trading
Yiu Kuen Tse, School of Economics, Singapore Management University

This paper applies the Asymmetric Autoregressive Conditional Duration (AACD) model of Bauwens and Giot (2003) to estimate the probability of informed trading (PIN) using irregularly spaced transaction data. We model trade direction (buy versus sell orders) and the duration between trades jointly. Unlike the Easley, Hvidkjaer and O'Hara (2002) approach, which uses the aggregate numbers of daily buy and sell orders to estimate PIN, our methodology allows for interactions between consecutive buy-sell orders and accounts for the duration between trades and the volume of trade. We extend the Easley-Hvidkjaer-O'Hara framework by allowing the probabilities of good news and bad news to vary each day. Our PIN estimates can be computed daily as well as over intraday intervals.

Using high-frequency transaction data to estimate the probability of informed trading by Anthony Tay, Christopher Ting, Yiu Kuen Tse and Mitch Warachka

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