International Journal of Theoretical and Applied Finance

This paper proposes a solution method for the discrete-time long-term dynamic portfolio optimization problem with state and asset allocation constraints. We use the ideas of Model Predictive Control (MPC) to solve the constrained stochastic control problem. MPC is a solution technique which was developed to solve constrained optimal control problems for deterministic control applications. MPC solves the optimal control problem with a receding horizon where a series of consecutive open-loop optimal control problems is solved.

The aim of this paper is to develop an MPC approach to the problem of long-term portfolio optimization when the expected returns of the risky assets are modeled using a factor model based on stochastic Gaussian processes. We prove that MPC is a suboptimal control strategy for stochastic systems which uses the new information advantageously and thus is better than the pure optimal open-loop control. For the open-loop optimal control optimization, we derive the conditional portfolio distribution and the corresponding conditional portfolio mean and variance. The mean and the variance depend on future decision about the asset allocation.

For the dynamic portfolio optimization problem, we consider constraints on the asset allocation as well as probabilistic constraints on the attainable values of the portfolio wealth. We discuss two different objectives, a classical mean–variance objective and the objective to maximize the probability of exceeding a predetermined value of the portfolio. The dynamic portfolio optimization problem is stated, and the solution via MPC is explained in detail. The results are then illustrated in a case study.

We examine the relative risk performance of the Dow Jones Islamic Index (DJIS) and find that the index outperforms the Dow Jones (DJIM) WORLD Index in terms of risk. Using the most recent Value-at-Risk (VaR) methodologies (RiskMetrics, Student-t APARCH, and skewed Student-t APARCH) on the 1996–2005 period, and assuming one-day holding period for both indices with a moving window of 500 day data, we show that the value of VaR is greater for DJIM WORLD than for DJIS Islamic. We interpret the results mainly to the profit-and-loss sharing principle of Islamic finance where banks share the profits and bear losses (Mudarabah) or share both profits and losses (Musharaka) with the firm.

Stock splits are a relatively new phenomenon in the Indian context. This paper examines the market effect of stock splits on stock price, return, volatility, and trading volume around the split ex-dates for a sample of stock splits undertaken in the Indian stock market over the period 1999–2005.

The traditional view of stock splits as cosmetic transactions that simply divide the same pie into more slices is inconsistent with the significant wealth effect associated with the announcement of a stock split. However, the empirical evidence confirms a negative effect on price and return of stock splits. The overall cumulative abnormal returns after the split are negative. These results suggest that stock splits have induced the market to revise its optimistic valuation about future firm performance, rejecting signaling hypothesis to which splits convey positive information to markets. Hence, stock splits have reduced the wealth of the shareholders. The results also show that presence of a positive effect on volatility and trading volume following the split events, thus suggesting that split events enhance liquidity.

We analyze and compare the performance of the Fourier transform method in affine and quadratic term structure models. We explain why the method of the reduction to FFT in dimension 1 is efficient for ATSMs of type A₀(n), but may lead to sizable errors for QTSMs unless computational errors are taken into account properly. We suggest a certain improvement and generalization which make FFT more accurate and, for the same precision, faster than the Leippold and Wu [M. Leippold and L. Wu, Option pricing under the quadratic class, Journal of Financial and Quantitative Analysis37(2) (2002) 271–295] method. We deduce simple general recommendations for the choice of parameters of computational schemes for QTSMs, which ensure a given precision, and an approximate formula for the bias which FFT produces.

We investigate the gains obtained by using GRID, an innovative web-based technology for parallel computing, in a Risk Management application. We show, by estimating a parametric Value at Risk, how GRID computing offers an opportunity to enhance the solution of computationally demanding problems with decentralized data retrieval. Furthermore, we also provide an analysis of the risk factors in the US market, by empirically testing, on the Fama and French database, a classic one factor model augmented with a time varying specification of beta.

Efficient numerical methods for pricing American options using Heston's stochastic volatility model are proposed. Based on this model the price of a European option can be obtained by solving a two-dimensional parabolic partial differential equation. For an American option the early exercise possibility leads to a lower bound for the price of the option. This price can be computed by solving a linear complementarity problem. The idea of operator splitting methods is to divide each time step into fractional time steps with simpler operators. This paper proposes componentwise splitting methods for solving the linear complementarity problem. The basic componentwise splitting decomposes the discretized problem into three linear complementarity problems with tridiagonal matrices. These problems can be efficiently solved using the Brennan and Schwartz algorithm, which was originally introduced for American options under the Black and Scholes model. The accuracy of the componentwise splitting method is increased by applying the Strang symmetrization. The good accuracy and the computational efficiency of the proposed symmetrized splitting method are demonstrated by numerical experiments.

We propose three analytic approximation methods for numerical valuation of the guaranteed annuity options in deferred annuity pension policies. The approximation methods include the stochastic duration approach, Edgeworth expansion, and analytic approximation in affine diffusions. The payoff structure in the annuity policies is similar to a quanto call option written on a coupon-bearing bond. To circumvent the limitations of the one-factor interest rate model, we model the interest rate dynamics by a two-factor affine interest rate term structure model. The numerical accuracy and the computational efficiency of these approximation methods are analyzed. We also investigate the value sensitivity of the guaranteed annuity option with respect to different parameters in the pricing model.

This paper derives the multi-period fair actuarial values for six deductible insurance policies offered in today's insurance markets. The loss in any given period is generated by the Weibull distribution with a known shape parameter but an unknown scale parameter. The insurer is assumed to be a Bayesian decision maker, in the sense that he/she learns sequentially about the unknown scale parameter by observing the realizations of the filed claims. It is shown that the insurer's underlying predictive loss distributions belong to the Burr family, and the multi-period actuarially fair policy value can be derived. With a proper loading, an insurance premium can be quoted. Our major contribution is the analytical derivations of the fair actuarial values for deductible insurance policies in the presence of parameter uncertainty and Bayesian learning.