A systematic review on the effectiveness of physical and rehabilitation interventions for chronic non-specific low back pain

Low back pain (LBP) is a common and disabling disorder in western society. The management of LBP comprises a range of different intervention strategies including surgery, drug therapy, and non-medical interventions. The objective of the present study is to determine the effectiveness of physical and rehabilitation interventions (i.e. exercise therapy, back school, transcutaneous electrical nerve stimulation (TENS), low level laser therapy, education, massage, behavioural treatment, traction, multidisciplinary treatment, lumbar supports, and heat/cold therapy) for chronic LBP. The primary search was conducted in MEDLINE, EMBASE, CINAHL, CENTRAL, and PEDro up to 22 December 2008. Existing Cochrane reviews for the individual interventions were screened for studies fulfilling the inclusion criteria. The search strategy outlined by the Cochrane Back Review Groups (CBRG) was followed. The following were included for selection criteria: (1) randomized controlled trials, (2) adult (≥18 years) population with chronic (≥12 weeks) non-specific LBP, and (3) evaluation of at least one of the main clinically relevant outcome measures (pain, functional status, perceived recovery, or return to work). Two reviewers independently selected studies and extracted data on study characteristics, risk of bias, and outcomes at short, intermediate, and long-term follow-up. The GRADE approach was used to determine the quality of evidence. In total 83 randomized controlled trials met the inclusion criteria: exercise therapy (n = 37), back school (n = 5), TENS (n = 6), low level laser therapy (n = 3), behavioural treatment (n = 21), patient education (n = 1), traction (n = 1), and multidisciplinary treatment (n = 6). Compared to usual care, exercise therapy improved post-treatment pain intensity and disability, and long-term function. Behavioural treatment was found to be effective in reducing pain intensity at short-term follow-up compared to no treatment/waiting list controls. Finally, multidisciplinary treatment was found to reduce pain intensity and disability at short-term follow-up compared to no treatment/waiting list controls. Overall, the level of evidence was low. Evidence from randomized controlled trials demonstrates that there is low quality evidence for the effectiveness of exercise therapy compared to usual care, there is low evidence for the effectiveness of behavioural therapy compared to no treatment and there is moderate evidence for the effectiveness of a multidisciplinary treatment compared to no treatment and other active treatments at reducing pain at short-term in the treatment of chronic low back pain. Based on the heterogeneity of the populations, interventions, and comparison groups, we conclude that there are insufficient data to draw firm conclusion on the clinical effect of back schools, low-level laser therapy, patient education, massage, traction, superficial heat/cold, and lumbar supports for chronic LBP

Non-parametric partial importance sampling for financial derivative pricing

Importance sampling is a promising variance reduction technique for Monte Carlo simulation-based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm that estimates the optimal proposal non-parametrically using a multivariate frequency polygon estimator. In contrast to parametric methods, non-parametric estimation allows for close approximation of the optimal proposal. Standard non-parametric importance sampling is inefficient for high-dimensional problems. We solve this issue by applying the procedure to a low-dimensional subspace, which is identified through principal component analysis and the concept of the effective dimension. The mean square error properties of the algorithm are investigated and its asymptotic optimality is shown. Quasi-Monte Carlo is used for further improvement of the method. It is easy to implement, particularly it does not require any analytical computation, and it is computationally very efficient. We demonstrate through path-dependent and multi-asset option pricing problems that the algorithm leads to significant efficiency gains compared with other algorithms in the literature.Monte Carlo methods, Pricing of derivatives securities, Path-dependent options, Option pricing via simulation, Financial engineering,

Generic pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility

We consider the pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility, for which we use a generic multi-currency framework. We allow for a general correlation structure between the drivers of the volatility, the inflation index, the domestic (nominal) and the foreign (real) rates. Having the flexibility to correlate the underlying FX/inflation/stock index with both stochastic volatility and stochastic interest rates yields a realistic model that is of practical importance for the pricing and hedging of options with a long-term exposure. We derive explicit valuation formulas for various securities, such as vanilla call/put options, forward starting options, inflation-indexed swaps and inflation caps/floors. These vanilla derivatives can be valued in closed form under Schobel and Zhu [Eur. Finance Rev., 1999, 4, 23-46] stochastic volatility, whereas we devise an (Monte Carlo) approximation in the form of a very effective control variate for the general Heston [Rev. Financial Stud., 1993, 6, 327-343] model. Finally, we investigate the quality of this approximation numerically and consider a calibration example to FX and inflation market data.Foreign Exchange, Inflation, Equity, Stochastic volatility, Stochastic interest rates, Hybrids,