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

Zero Jordan product determined Banach algebras

A Banach algebra $A$ is said to be a zero Jordan product determined Banach algebra if every continuous bilinear map $\varphi\colon A\times A\to X$, where $X$ is an arbitrary Banach space, which satisfies $\varphi(a,b)=0$ whenever $a$, $b\in A$ are such that $ab+ba=0$, is of the form $\varphi(a,b)=\sigma(ab+ba)$ for some continuous linear map $\sigma$. We show that all $C^*$-algebras and all group algebras $L^1(G)$ of amenable locally compact groups have this property, and also discuss some applications

Presencia de estratificación cruzada Hummocky en depósitos lacustres del Terciario de la Depresión del Ebro

En algunos depósitos carbonatado-terrígenos del Terciario lacustre de la Depresión del Ebro se han reconocido estructuras sedimentarias generadas por olas entre las que se han identificado ripples de oscilación así como estratificaciones cruzadas «Hummocky» y «Swaley» que evidencian etapas de alta energía. Las investigaciones realizadas ponen de manifiesto que las facies de «ripples» y «hummocky» pudieron originarse entre profundidades de 1 y 7 m bajo la acción de vientos de 50 km/h como mínimo. Los materiales estudiados son afectados por fallas sin sedimentarias con superficies lístricas de 1,5 m de salto. Las capas con HCS fosilizan estas fallas o están cerca de los estratos que las recubren. Por tanto, en la génesis de las facies de HCS se puede considerar la posible acción de «tsunamis» lacustres conectados con la inestabilidad sin sedimentaria provocada por las fallas antes mencionadas

Evolución paleogeográfica de los conglomerados miocenos adosados al borde norte de la Sierra de Cameros. (La Rioja)

Three Tectosedimentary Units (TSL! A,, A, and A,) were identified in the tertiary conglomeratic facies, which are croping out in Sierra de Yerga, Cabi Monteros and Serradero (southem margin of the Ebro Basin, adjoining the Sierra de Carneros; fig. 1). The first and third TSU have a fining upward evolution; the second one has a cyclic evolution (fining-coarsening upward). Correlation between these TSU with those established in eastern sectors of the Ebro Basin allowed us to date them.The three TSU range from middle Aragonian to Turolian (Middle to Upper Aragonian, Upper Aragonian to Vallesian and Vallesian to Turolian, respectively). These units were deposited under compressive stress as evidenced by both, vertical evolution of sedimentary units and their relationship to active tectonic structures. Sierra de Carneros thrust affects the first and second TSI;, whereas this thrust is fossilized by the third one. This relationship shows that the age for the end of the compression was, at least, Vallesian. However, Carneros thrust maybe reached the Turolian in adecelerate way. Tmportant horizontal translation of the Sierra de Carneros thrust is detected at the diastrophic maximum which was developed at the onset of the first TSU. Alluvial fans of high transport efficiency, are associated to this horizontal translation. The source areafor these alluvial systems was mainly siliceous in composition (i. e., Purbeck-Weald facies). On the contrary, vertical translation along this trust prevails at two penods of diastrophic maximum which are located at the boundaries of both, the first and second TSU and the second and third TSU, respectively. Alluvial fans of low transport efficiency, which had mainly carbonate units in their source areas (i. e., Jurassic units), are linked to this vertical translation