Recovering implied risk-neutral probability density function using SVR

Using support vector regression （SVR）, a novel non-parametric method for recovering implied risk-neutral probability density function （IRNPDF） is investigated by solving linear operator equations. First, the SVR principle for function approximation is introduced, and an SVR method for solving linear operator equations with knowing some values of the right-hand function and without knowing its form is depicted. Then, the principle for solving the IRNPDF based on SVR and the method for constructing cross-kernel functions are proposed. Finally, an empirical example is given to verify the validity of the method. The results show that the proposed method can overcome the shortcomings of the traditional parametric methods, which have strict restrictions on the option exercise price; meanwhile, it requires less data than other non-parametric methods, and it is a promising method for the recover of IRNPDF.

Long-Term Trends in the Probability of Different Grades of Haze Days in China from 1960 to 2013

The number of haze days and daily visibility data for 543 stations in China were used to define the probabilities of four grades of haze days:slight haze(SLH)days;light haze(LIH)days;moderate haze(MOH)days;and severe haze(SEH)days.The change trends of the four grades of haze were investigated and the following results were obtained.The highest probability was obtained for SLH days(95.138%),which showed a decreasing trend over the last54 years with the fastest rate of decrease of-0.903%·(10 years)-1 and a trend coefficient of-0.699,passing the 99.9%confidence level.The probabilities of LIH and MOH days increased steadily,whereas the probability of SEH days showed a slight downward trend during that period.The increasing probability of SLH days was mainly distributed to the east of 105°E and the south of 42°N and the highest value of the trend coefficient was located in the Pearl River Delta and Yangtze River Delta regions.The increasing probability of LIH days was mainly distributed in eastern China and the southeastern coastal region.The probabilities of MOH and SEH days was similar to the probability of LIH days.An analysis of the four grades of haze days in cities with different sizes suggested that the probability of SLH days in large cities and medium cities clearly decreased during the last 54 years.However,the probabilities of LIH days was<10%and increased steadily.The probability of MOH days showed a clear interdecadal fluctuation and the probability of SEH days showed a weak upward trend.The probability of SLH days in small cities within 0.8°of large or medium cities decreased steadily,but the probability of LIH and MOH days clearly increased,which might be attributed to the impact of large and medium cities.The probability of SLH days in small cities>1.5°from a large or medium city showed an increasing trend and reached 100%after 1990;the probability of the other three grades was small and decreased significantly.

Spatial and temporal synthesized probability gain for middle and long-term earthquake forecast and its preliminary application

The principle of middle and long-term earthquake forecast model of spatial and temporal synthesized probability gain and the evaluation of forecast efficiency (R-values) of various forecast methods are introduced in this paper. The R-value method, developed by Xu (1989), is further developed here, and can be applied to more complicated cases. Probability gains in spatial and/or temporal domains and the R-values for different forecast methods are estimated in North China. The synthesized probability gain is then estimated as an example.

Using the Analytic Hierarchy Process in Long-Term Load Growth Forecast

The load growth is the most important uncertainties in power system planning process. The applications of the classical long-term load forecasting methods particularly applied to utilities in transition economy are insufficient and may produce incorrect decisions in power system planning process. This paper discusses using the method of analytic hierarchy process to calculate the probability distribution of load growth obtained previously by standard load forecasting methods.

Calculating collision probability for long-term satellite encounters through the reachable domain method

ABSTRACT Satellite encounters during close operations,such as rendezvous,formation,and cluster flights,are typical long-term encounters.The collision probability in such an encounter is a primary safety concern.In this study,a parametric method is proposed to compute the long-term collision probability for close satellite operations with initial state uncertainty.Random relative state errors resulting from system uncertainty lead to possible deviated trajectories with respect to the nominal one.To describe such a random event meaningfully,each deviated trajectory sample should be mapped to a unique and time-independent element in a random variable(RV)space.In this study,the RV space was identified as the transformed state space at a fixed initial time.The physical dimensions of both satellites were characterized by a combined hard-body sphere.Transforming the combined hard-body sphere into the RV space yielded a derived ellipsoid,which evolved over time and swept out a derived collision volume.The derived collision volume was solved using the reachable domain method.Finally,the collision probability was computed by integrating a probability density function over the derived collision volume.The results of the proposed method were compared with those of a nonparametric computation-intensive Monte Carlo method.The relative difference between the two results was found to be<0.6%,verifying the accuracy of the proposed method.

A generalization of exotic options pricing formulae

Exotic options, or “path-dependent” options are options whose payoff depends on the behavior of the price of the underlying between 0 and the maturity, rather than merely on the final price of the underlying, such as compound options, reset options and so on. In this paper, a generalization of the Geske formula for compound call options is obtained in the case of time-dependent volatility and time-dependent interest rate by applying martingale methods and the change of numeraire or the change of probability measure. An analytic formula for the reset call options with predetermined dates is also derived in the case by using the same approach. In contrast to partial differential equation (PDE) approach, our approach is simpler.

Analysis of the Impact of Large Constellations on the Space Debris Environment and Countermeasures

Large constellations have developed rapidly in recent years because of their unique advantages, but they will inevitably have a major negative impact on the space debris environment, leading to its deterioration. The key to mitigate the impact is the success rate and duration of the post-mission disposal(PMD) process. Aiming at solving this problem, this paper further studies the impact of large constellations on other space assets under different PMD strategies through simulation, and proposes corresponding strategies and suggestions for mitigation.According to One Web’s large constellation launch plan, the dangerous intersection of the large constellation with existing space assets at different stages of the constellations life cycle is calculated by simulation. Based on this, the influence of the large constellation operation on existing space assets at different times and strategies of PMD is analyzed. The conclusion shows that in the PMD stage, large constellations have the greatest impact on existing space assets;the PMD duration and number of satellites performing PMD at the same time are key factors to the degree of negative impact. The faster the PMD is, the less threat it poses to other spacecraft. More results and conclusions are still being analyzed.