A semi-analytic method for valuing high-dimensional options on the maximum and minimum of multiple assets

Valuing high-dimensional options has many important applications in finance but when the true distributions are unknown or complex, numerical approximations must be used. Approximation methods based on Monte-Carlo simulation show a steep trade-off between estimation accuracy and computational efficiency. This article presents an alternative semi-analytic approximation method for pricing options on the maximum or minimum of multiple assets with unknown distributions. Computational efficiency is shown to improve significantly without sacrificing estimation accuracy. The method is illustrated with applications to options on underlying assets with mean-reverting prices, time-dependent correlations, and stochastic volatility The authors would like to thank the two anonymous referees, the associate editor, and Dr. Jess H. Chua at the University of Calgary for valuable comments and insights on this research. This research was partly supported by NUS grant R-146-000-059-112     

On improving the least squares Monte Carlo option valuation method

This paper studies various possible approaches to improving the least squares Monte Carlo option valuation method. We test different regression algorithms and suggest a variation to estimating the option continuation value, which can reduce the execution time of the algorithm by one third. We test the choice of varying polynomial families with different number of basis functions. We compare several variance reduction techniques, and find that using low discrepancy sequences can improve the accuracy up to four times. We also extend our analysis to compound and mutually exclusive options. For the latter, we propose an improved algorithm which is faster and more accurate.     

Approximation of Asymmetric Multivariate Return Distributions

We develop a new method to approximate the asymmetric multivariate probability density function (pdf) of financial asset returns by using series expansions; a rate of convergence for the mean absolute error of this approximation is also provided. We then propose the method of maximum likelihood and the generalized method of moments to estimate the parameters of the approximated pdf. A Monte-Carlo experiment corroborates the feasibility of our approach.     

Portfolio Inefficiency and the Cross-section of Expected Returns

The Capital Asset Pricing Model implies that (i) the market portfolio is efficient and (ii) expected returns are linearly related to betas. Many do not view these implications as separate, since either implies the other, but we demonstrate that either can hold nearly perfectly while the other fails grossly. If the index portfolio is inefficient, then the coefficients and $R^2$ from an ordinary least squares regression of expected returns on betas can equal essentially any values and bear no relation to the index portfolio's mean-variance location. That location does determine the outcome of a mean-beta regression fitted by generalized least squares.     

Portfolio optimization in discrete time with proportional transaction costs under stochastic volatility

This paper is devoted to evaluating the optimal self-financing strategy and the optimal trading frequency for a portfolio with a risky asset and a risk-free asset. The objective is to maximize the expected future utility of the terminal wealth in a stochastic volatility setting, when transaction costs are incurred at each discrete trading time. A HARA utility function is used, allowing a simple approximation of the optimization problem, which is implementable forward in time. For each of various transaction cost rates, we find the optimal trading frequency, i.e. the one that attains the maximum of the expected utility at time zero. We study the relation between transaction cost rate and optimal trading frequency. The numerical method used is based on a stochastic volatility particle filtering algorithm, combined with a Monte-Carlo method. The filtering algorithm updates the estimate of the volatility distribution forward in time, as new stock observations arrive; these updates are used at each of these discrete times to compute the new portfolio allocation.     

A Comparison of State-of-the-Art Classification Techniques for Expert Automobile Insurance Claim Fraud Detection

Several state‐of‐the‐art binary classification techniques are experimentally evaluated in the context of expert automobile insurance claim fraud detection. The predictive power of logistic regression, C4.5 decision tree, k‐nearest neighbor, Bayesian learning multilayer perceptron neural network, least‐squares support vector machine, naive Bayes, and tree‐augmented naive Bayes classification is contrasted. For most of these algorithm types, we report on several operationalizations using alternative hyperparameter or design choices. We compare these in terms of mean percentage correctly classified (PCC) and mean area under the receiver operating characteristic (AUROC) curve using a stratified, blocked, ten‐fold cross‐validation experiment. We also contrast algorithm type performance visually by means of the convex hull of the receiver operating characteristic (ROC) curves associated with the alternative operationalizations per algorithm type. The study is based on a data set of 1,399 personal injury protection claims from 1993 accidents collected by the Automobile Insurers Bureau of Massachusetts. To stay as close to real‐life operating conditions as possible, we consider only predictors that are known relatively early in the life of a claim. Furthermore, based on the qualification of each available claim by both a verbal expert assessment of suspicion of fraud and a ten‐point‐scale expert suspicion score, we can compare classification for different target/class encoding schemes. Finally, we also investigate the added value of systematically collecting nonflag predictors for suspicion of fraud modeling purposes. From the observed results, we may state that: (1) independent of the target encoding scheme and the algorithm type, the inclusion of nonflag predictors allows us to significantly boost predictive performance; (2) for all the evaluated scenarios, the performance difference in terms of mean PCC and mean AUROC between many algorithm type operationalizations turns out to be rather small; visual comparison of the algorithm type ROC curve convex hulls also shows limited difference in performance over the range of operating conditions; (3) relatively simple and efficient techniques such as linear logistic regression and linear kernel least‐squares support vector machine classification show excellent overall predictive capabilities, and (smoothed) naive Bayes also performs well; and (4) the C4.5 decision tree operationalization results are rather disappointing; none of the tree operationalizations are capable of attaining mean AUROC performance in line with the best. Visual inspection of the evaluated scenarios reveals that the C4.5 algorithm type ROC curve convex hull is often dominated in large part by most of the other algorithm type hulls.     

Robust Estimation of Beta Coefficients: Evidence from a Small Stock Market

In this paper we demonstrate that robust estimators improve the reliability of estimates of beta coefficients on small, thinly traded stock markets. We outline several different types of robust and bounded influence regression estimators and assess them using a jackknife methodology on data from the Johannesburg Stock Exchange. The empirical evidence confirms the hypothesis that robust estimators are more efficient than least squares estimators and indicates that least squares estimators may over-estimate systematic risk in some cases.