Option Pricing beyond Black-Scholes Model: Quantum Mechanics Approach

Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can take various unexpected market behaviors into account to modify the option pricing. As examples, we present several market forces to analyze their effects on the option pricing. These results provide us two practical applications. One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging. The other implies the existence of some risk premium when some unexpected forces emerge

Finding unprecedentedly low-thermal-conductivity half-Heusler semiconductors via high-throughput materials modeling

The lattice thermal conductivity ({\kappa}{\omega}) is a key property for many potential applications of compounds. Discovery of materials with very low or high {\kappa}{\omega} remains an experimental challenge due to high costs and time-consuming synthesis procedures. High-throughput computational pre-screening is a valuable approach for significantly reducing the set of candidate compounds. In this article, we introduce efficient methods for reliably estimating the bulk {\kappa}{\omega} for a large number of compounds. The algorithms are based on a combination of machine-learning algorithms, physical insights, and automatic ab-initio calculations. We scanned approximately 79,000 half-Heusler entries in the AFLOWLIB.org database. Among the 450 mechanically stable ordered semiconductors identified, we find that {\kappa}{\omega} spans more than two orders of magnitude- a much larger range than that previously thought. {\kappa}{\omega} is lowest for compounds whose elements in equivalent positions have large atomic radii. We then perform a thorough screening of thermodynamical stability that allows to reduce the list to 77 systems. We can then provide a quantitative estimate of {\kappa}{\omega} for this selected range of systems. Three semiconductors having {\kappa}{\omega} < 5 W /(m K) are proposed for further experimental study.Comment: 9 pages, 4 figure