The Pricing of Multiple-Expiry Exotics

In this paper we extend Buchen's method to develop a new technique for pricing of some exotic options with several expiry dates(more than 3 expiry dates) using a concept of higher order binary option. At first we introduce the concept of higher order binary option and then provide the pricing formulae of $n$-th order binaries using PDE method. After that, we apply them to pricing of some multiple-expiry exotic options such as Bermudan option, multi time extendable option, multi shout option and etc. Here, when calculating the price of concrete multiple-expiry exotic options, we do not try to get the formal solution to corresponding initial-boundary problem of the Black-Scholes equation, but explain how to express the expiry payoffs of the exotic options as a combination of the payoffs of some class of higher order binary options. Once the expiry payoffs are expressed as a linear combination of the payoffs of some class of higher order binary options, in order to avoid arbitrage, the exotic option prices are obtained by static replication with respect to this family of higher order binaries.Comment: 16 pages, 3 figures, Ver. 1 was presented in the 1st International Conference of Pyongyang University of Science & Technology, 5~6, Oct, 2011, in ver. 2 added proof, in ver. 3 revised and added some detail of proofs, Ver. 4,5: latex version, Ver. 6~8: corrected typos in EJMAA Vol.1(2)2013,247-25

A generalized scheme for BSDEs based on derivative approximation and its error estimates

In this paper we propose a generalized numerical scheme for backward stochastic differential equations(BSDEs). The scheme is based on approximation of derivatives via Lagrange interpolation. By changing the distribution of sample points used for interpolation, one can get various numerical schemes with different stability and convergence order. We present a condition for the distribution of sample points to guarantee the convergence of the scheme.Comment: 11 pages, 1 table. arXiv admin note: text overlap with arXiv:1808.0156

A Numerical Scheme For High-dimensional Backward Stochastic Differential Equation Based On Modified Multi-level Picard Iteration

In this paper, we propose a new kind of numerical scheme for high-dimensional backward stochastic differential equations based on modified multi-level Picard iteration. The proposed scheme is very similar to the original multi-level Picard iteration but it differs on underlying Monte-Carlo sample generation and enables an improvement in the sense of complexity. We prove the explicit error estimates for the case where the generator does not depend on control variate

Stochastic Gronwall's inequality in random time horizon and its application to BSDE

In this paper, we introduce and prove a stochastic Gronwall's inequality in (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random terminal time under stochastic monotonicity condition

Adapted θ\theta-Scheme and Its Error Estimates for Backward Stochastic Differential Equations

In this paper we propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional $\theta$-scheme, we reduce truncation errors by taking $\theta$ carefully for every subinterval according to the characteristics of integrands. We give error estimates of this nonlinear scheme and verify the order of scheme through a typical numerical experiment.Comment: 18 pages, 3 tables, 1 figur

A new distance law of planets and satellites in the solar system

In the 1960s, it has been substantiated that an equation of Schrodinger type could describe the diffusion phenomena, and the main consequence from this finding has been that there would be wave property in the diffusion processes as well. This theory has been immediately proved through laboratorial experiments. Afterwards the theory was applied to the primordial nebula which was thought to surround the protosun, and has found the consistency of the prediction of the theory with current distance distribution of the planets to be excellent. At the end of 20th century new satellites of planets were discovered. On the basis of the new data, the theory is tested thoroughly and the result allows us to come to the conclusion that the basic process for the distances of the planets from the protosun to be determined has been the diffusion of the primordial nebula consisting of mainly molecular gas.Comment: 24 pages, 5 table

Modeling of Volatility with Non-linear Time Series Model

In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its parameter estimation is studied.Comment: 8 page

A Stable Minutia Descriptor based on Gabor Wavelet and Linear Discriminant Analysis

The minutia descriptor which describes characteristics of minutia, plays a major role in fingerprint recognition. Typically, fingerprint recognition systems employ minutia descriptors to find potential correspondence between minutiae, and they use similarity between two minutia descriptors to calculate overall similarity between two fingerprint images. A good minutia descriptor can improve recognition accuracy of fingerprint recognition system and largely reduce comparing time. A good minutia descriptor should have high ability to distinguish between different minutiae and at the same time should be robust in difficult conditions including poor quality image and small size image. It also should be effective in computational cost of similarity among descriptors. In this paper, a robust minutia descriptor is constructed using Gabor wavelet and linear discriminant analysis. This minutia descriptor has high distinguishing ability, stability and simple comparing method. Experimental results on FVC2004 and FVC2006 databases show that the proposed minutia descriptor is very effective in fingerprint recognition

The Binomial Tree Method and Explicit Difference Schemes for American Options with Time Dependent Coefficients

Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that the dynamics of the underlying asset's price forms a binomial tree if a partition of time interval with equal parts is used. A time interval partition method that allows binomial tree dynamics of the underlying asset's price is provided. Conditions under which the prices of American option by BTM and EDS have the monotonic property on time variable are found. Using convergence of EDS for variational inequality model of American options to viscosity solution the decreasing property of the price of American put options and increasing property of the optimal exercise boundary on time variable are proved. First, put options are considered. Then the linear homogeneity and call-put symmetry of the price functions in the BTM and the EDS for the variational inequality model of American options with time dependent coefficients are studied and using them call options are studied.Comment: 39 pages, 4 figures; In this version, some new results for American call options are added in Sections 6,7 and

Apparent Positions of Planets

The apparent positions of planets are determined by means of the fundamental ephemerides, the precession-nutation models of the Earth, the gravitational effects and aberrations et al. Around 2000, many astrometrical conceptions, models and theories had been newly defined and updated:for the fiducial celestial reference system, the ICRS is introduced, the fundamental ephemerides - DE405/LE405 et al.,precession-nutation model - IAU 2000A/IAU 2006 model. Using the traditional algorithm and the updated models, we develop the system of calculating the apparent positions of planets. The results are compared with the Astronomical Almanac and proved in their correctness.Comment: 9 pages, 3 figure