Term Structure Movements Implicit in Option Prices

This paper analyzes how including options in the estimation of a dynamic term structure model impacts the way it captures term structure movements. Two versions of a multi-factor Gaussian model are compared: One adopting only bonds data, and the other adopting a joint dataset of bonds and options. Term structure movements extracted under each version behave distinctly, with slope and curvature presenting higher mean reversion rates when options are adopted. The composition of bond risk premium is also affected, with considerably more weight attributed to the level factor when options are included. The inclusion of options in the estimation of the dynamic model also improves the pricing of out-of-sample options.

Identifying Volatility Risk Premium from Fixed Income Asian Options

We provide approximation formulas for at-the-money asian option prices to extract volatility risk premium from a joint dataset of bonds and option prices. The dynamic model generates stochastic volatility and a time-varying volatility risk premium, which explicitly depends on the average cross section of bond yields and on the time series behavior of option prices. When estimated using a joint dataset of Brazilian local bonds and asian options, the model generates bond risk premium strongly correlated (89%) with a widely accepted emerging markets benchmark index, and a negative volatility risk premium implying that investors might be using options as insurance in this market. Volatility premium explains a significant portion (32.5%) of bond premium, confirming that options are indeed important to identify risk premium in dynamic term structure models.

Simplified game of life: Algorithms and complexity

Game of Life is a simple and elegant model to study dynamical system over networks. The model consists of a graph where every vertex has one of two types, namely, dead or alive. A configuration is a mapping of the vertices to the types. An update rule describes how the type of a vertex is updated given the types of its neighbors. In every round, all vertices are updated synchronously, which leads to a configuration update. While in general, Game of Life allows a broad range of update rules, we focus on two simple families of update rules, namely, underpopulation and overpopulation, that model several interesting dynamics studied in the literature. In both settings, a dead vertex requires at least a desired number of live neighbors to become alive. For underpopulation (resp., overpopulation), a live vertex requires at least (resp. at most) a desired number of live neighbors to remain alive. We study the basic computation problems, e.g., configuration reachability, for these two families of rules. For underpopulation rules, we show that these problems can be solved in polynomial time, whereas for overpopulation rules they are PSPACE-complete

Lønpræmie for lønmodtagere dækket af en overenskomst? Danmark som case

Udenlandske studier, primært i USA og England, har påvist, at lønmodtagere, der er medlem af en fagforening, får en lønpræmie i forhold til lønmodtagere, der ikke er medlem af en fagforening. Det vil sige, at der opnås en lønmæssig gevinst ved at være fagforeningsmedlem sammenlignet med ikke at være det. I artiklen her undersøger vi, på baggrund af et unikt dansk empirisk løndatamateriale, om de udenlandske resultater genfindes på det danske arbejdsmarked. Vores undersøgelse viser, at overenskomstdækning giver faggrupperne i bunden af lønhierarkiet de største løngevinster og giver en samlet, gennemsnitlig løngevinst for lønmodtagere, der er dækket af en kollektiv overenskomst sammenlignet med lønmodtagere, der ikke er overenskomstdækket

Strategy complexity of concurrent safety games

We consider two player, zero-sum, finite-state concurrent reachability games, played for an infinite number of rounds, where in every round, each player simultaneously and independently of the other players chooses an action, whereafter the successor state is determined by a probability distribution given by the current state and the chosen actions. Player 1 wins iff a designated goal state is eventually visited. We are interested in the complexity of stationary strategies measured by their patience, which is defined as the inverse of the smallest non-zero probability employed. Our main results are as follows: We show that: (i) the optimal bound on the patience of optimal and -optimal strategies, for both players is doubly exponential; and (ii) even in games with a single non-absorbing state exponential (in the number of actions) patience is necessary

Faster Monte-Carlo algorithms for fixation probability of the moran process on undirected graphs

Evolutionary graph theory studies the evolutionary dynamics in a population structure given as a connected graph. Each node of the graph represents an individual of the population, and edges determine how offspring are placed. We consider the classical birth-death Moran process where there are two types of individuals, namely, the residents with fitness 1 and mutants with fitness r. The fitness indicates the reproductive strength. The evolutionary dynamics happens as follows: in the initial step, in a population of all resident individuals a mutant is introduced, and then at each step, an individual is chosen proportional to the fitness of its type to reproduce, and the offspring replaces a neighbor uniformly at random. The process stops when all individuals are either residents or mutants. The probability that all individuals in the end are mutants is called the fixation probability, which is a key factor in the rate of evolution. We consider the problem of approximating the fixation probability. The class of algorithms that is extremely relevant for approximation of the fixation probabilities is the Monte-Carlo simulation of the process. Previous results present a polynomial-time Monte-Carlo algorithm for undirected graphs when r is given in unary. First, we present a simple modification: instead of simulating each step, we discard ineffective steps, where no node changes type (i.e., either residents replace residents, or mutants replace mutants). Using the above simple modification and our result that the number of effective steps is concentrated around the expected number of effective steps, we present faster polynomial-time Monte-Carlo algorithms for undirected graphs. Our algorithms are always at least a factor O(n2/ log n) faster as compared to the previous algorithms, where n is the number of nodes, and is polynomial even if r is given in binary. We also present lower bounds showing that the upper bound on the expected number of effective steps we present is asymptotically tight for undirected graphs

Quantitative Verification on Product Graphs of Small Treewidth

Product graphs arise naturally in formal verification and program analysis. For example, the analysis of two concurrent threads requires the product of two component control-flow graphs, and for language inclusion of deterministic automata the product of two automata is constructed. In many cases, the component graphs have constant treewidth, e.g., when the input contains control-flow graphs of programs. We consider the algorithmic analysis of products of two constant-treewidth graphs with respect to three classic specification languages, namely, (a) algebraic properties, (b) mean-payoff properties, and (c) initial credit for energy properties. Our main contributions are as follows. Consider a graph G that is the product of two constant-treewidth graphs of size n each. First, given an idempotent semiring, we present an algorithm that computes the semiring transitive closure of G in time Õ(n4). Since the output has size Θ(n4), our algorithm is optimal (up to polylog factors). Second, given a mean-payoff objective, we present an O(n3)-time algorithm for deciding whether the value of a starting state is non-negative, improving the previously known O(n4) bound. Third, given an initial credit for energy objective, we present an O(n5)-time algorithm for computing the minimum initial credit for all nodes of G, improving the previously known O(n8) bound. At the heart of our approach lies an algorithm for the efficient construction of strongly-balanced tree decompositions of constant-treewidth graphs. Given a constant-treewidth graph G′ of n nodes and a positive integer λ, our algorithm constructs a binary tree decomposition of G′ of width O(λ) with the property that the size of each subtree decreases geometrically with rate (1/2 + 2-λ)

Optimal reachability and a space-time tradeoff for distance queries in constant-treewidth graphs

We consider data-structures for answering reachability and distance queries on constant-treewidth graphs with n nodes, on the standard RAM computational model with wordsize W = Θ(log n). Our first contribution is a data-structure that after O(n) preprocessing time, allows (1) pair reachability queries in O(1) time; and (2) single-source reachability queries in O(n/log n) time. This is (asymptotically) optimal and is faster than DFS/BFS when answering more than a constant number of single-source queries. The data-structure uses at all times O(n) space. Our second contribution is a space-time tradeoff data-structure for distance queries. For any ϵ ∈ [1/2,1], we provide a data-structure with polynomial preprocessing time that allows pair queries in O(n1-ϵ · α(n)) time, where α is the inverse of the Ackermann function, and at all times uses O(nϵ) space. The input graph G is not considered in the space complexity