Estimation of Risk-Neutral Density Surfaces

Option price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating risk-neutral densities associated with several maturities. Our method uses bicubic splines in order to achieve the desired smoothness for the estimation and an optimization model to choose the spline functions that best fit the price data. Semidefinite programming is employed to guarantee the nonnegativity of the densities. We illustrate the process using synthetic option price data generated using log-normal and absolute diffusion processes as well as actual price data for options on the S&P500 index. We also used the risk-neutral densities that we computed to price exotic options and observed that this approach generates prices that closely approximate the market prices of these options.

On the Nesterov-Todd Direction in Semidefinite Programming

On the Nesterov-Todd Direction in Semidefinite Programmin

Inhibition of breathing after surfactant depletion is achieved at a higher arterial PCO(2 )during ventilation with liquid than with gas

BACKGROUND: Inhibition of phrenic nerve activity (PNA) can be achieved when alveolar ventilation is adequate and when stretching of lung tissue stimulates mechanoreceptors to inhibit inspiratory activity. During mechanical ventilation under different lung conditions, inhibition of PNA can provide a physiological setting at which ventilatory parameters can be compared and related to arterial blood gases and pH. OBJECTIVE: To study lung mechanics and gas exchange at inhibition of PNA during controlled gas ventilation (GV) and during partial liquid ventilation (PLV) before and after lung lavage. METHODS: Nine anaesthetised, mechanically ventilated young cats (age 3.8 ± 0.5 months, weight 2.3 ± 0.1 kg) (mean ± SD) were studied with stepwise increases in peak inspiratory pressure (PIP) until total inhibition of PNA was attained before lavage (with GV) and after lavage (GV and PLV). Tidal volume (V(t)), PIP, oesophageal pressure and arterial blood gases were measured at inhibition of PNA. One way repeated measures analysis of variance and Student Newman Keuls-tests were used for statistical analysis. RESULTS: During GV, inhibition of PNA occurred at lower PIP, transpulmonary pressure (Ptp) and Vt before than after lung lavage. After lavage, inhibition of inspiratory activity was achieved at the same PIP, Ptp and Vt during GV and PLV, but occurred at a higher PaCO(2 )during PLV. After lavage compliance at inhibition was almost the same during GV and PLV and resistance was lower during GV than during PLV. CONCLUSION: Inhibition of inspiratory activity occurs at a higher PaCO(2 )during PLV than during GV in cats with surfactant-depleted lungs. This could indicate that PLV induces better recruitment of mechanoreceptors than GV

A randomised controlled trial investigating the effect of nutritional supplementation on visual function in normal, and age-related macular disease affected eyes: design and methodology [ISRCTN78467674]

BACKGROUND: Age-related macular disease is the leading cause of blind registration in the developed world. One aetiological hypothesis involves oxidation, and the intrinsic vulnerability of the retina to damage via this process. This has prompted interest in the role of antioxidants, particularly the carotenoids lutein and zeaxanthin, in the prevention and treatment of this eye disease. METHODS: The aim of this randomised controlled trial is to determine the effect of a nutritional supplement containing lutein, vitamins A, C and E, zinc, and copper on measures of visual function in people with and without age-related macular disease. Outcome measures are distance and near visual acuity, contrast sensitivity, colour vision, macular visual field, glare recovery, and fundus photography. Randomisation is achieved via a random number generator, and masking achieved by third party coding of the active and placebo containers. Data collection will take place at nine and 18 months, and statistical analysis will employ Student's t test. DISCUSSION: A paucity of treatment modalities for age-related macular disease has prompted research into the development of prevention strategies. A positive effect on normals may be indicative of a role of nutritional supplementation in preventing or delaying onset of the condition. An observed benefit in the age-related macular disease group may indicate a potential role of supplementation in prevention of progression, or even a degree reversal of the visual effects caused by this condition