Towards the quantification of the semantic information encoded in written language

Written language is a complex communication signal capable of conveying information encoded in the form of ordered sequences of words. Beyond the local order ruled by grammar, semantic and thematic structures affect long-range patterns in word usage. Here, we show that a direct application of information theory quantifies the relationship between the statistical distribution of words and the semantic content of the text. We show that there is a characteristic scale, roughly around a few thousand words, which establishes the typical size of the most informative segments in written language. Moreover, we find that the words whose contributions to the overall information is larger, are the ones more closely associated with the main subjects and topics of the text. This scenario can be explained by a model of word usage that assumes that words are distributed along the text in domains of a characteristic size where their frequency is higher than elsewhere. Our conclusions are based on the analysis of a large database of written language, diverse in subjects and styles, and thus are likely to be applicable to general language sequences encoding complex information.Comment: 19 pages, 4 figure

Option Pricing of Twin Assets

How to price and hedge claims on nontraded assets are becoming increasingly important matters in option pricing theory today. The most common practice to deal with these issues is to use another similar or "closely related" asset or index which is traded, for hedging purposes. Implicitly, traders assume here that the higher the correlation between the traded and nontraded assets, the better the hedge is expected to perform. This raises the question as to how \textquoteleft{}closely related\textquoteright{} the assets really are. In this paper, the concept of twin assets is introduced, focusing the discussion precisely in what does it mean for two assets to be similar. Our findings point to the fact that, in order to have very similar assets, for example identical twins, high correlation measures are not enough. Specifically, two basic criteria of similarity are pointed out: i) the coefficient of variation of the assets and ii) the correlation between assets. From here, a method to measure the level of similarity between assets is proposed, and secondly, an option pricing model of twin assets is developed. The proposed model allows us to price an option of one nontraded asset using its twin asset, but this time knowing explicitly what levels of errors we are facing. Finally, some numerical illustrations show how twin assets behave depending upon their levels of similarities, and how their potential differences will traduce in MAPE (mean absolute percentage error) for the proposed option pricing model