Person: Vilar Zanón, José Luis
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First Name
José Luis
Last Name
Vilar Zanón
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Económicas y Empresariales
Department
Economía Financiera, Actuarial y Estadística
Area
Economía Financiera y Contabilidad
Identifiers
3 results
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Item A linear goal programming method to recover risk neutral probabilities from options prices by maximum entropy(Decisions in Economics and Finance, 2019) Peraita Ezcurra, Olivia; Vilar Zanón, José LuisWe develop a new methodology to retrieve risk neutral probabilities (equivalent martingale measure) with maximum entropy from quoted option prices. We assume the no arbitrage hypothesis and model the efficient market hypothesis by means of a maximum entropic risk neutral distribution. The method is free of parametric assumption except for the simulation of the distribution support, for which purpose we can choose any stochastic model. Firstly, we innovate in the minimization of a different f-divergence than Kullback–Leibler’s relative entropy, resulting in the total variation distance. We minimize it by means of linear goal programming, thus guaranteeing a fast numerical resolution. The method values non-traded assets finding a RNP minimizing its f-divergence to the maximum entropy distribution over a simulated support—the uniform distribution—calibrated to the benchmarks prices constraints. Our second innovation is that in an incomplete market, we can increase the f-divergence from its minimum to obtain any asset price belonging to the interval satisfying the non-existence of an arbitrage portfolio, without presupposing any utility function for the decision maker. We exemplify our methodology by means of synthetic and real-world cases, showing that our methodology can either price non-traded assets or interpolate and extrapolate a volatility surface.Item Pricing Illiquid Assets by Entropy Maximization Through Linear Goal Programming(Mathematical and Statistical Methods for Actuarial Sciences and Finance, 2018) Peraita Ezcurra, Olivia; Vilar Zanón, José LuisIn this contribution we study the problem of retrieving a risk neutral probability (RNP) in an incomplete market, with the aim of pricing non-traded assets and hedging their risk. The pricing issue has been often addressed in the literature finding an RNP with maximum entropy by means of the minimization of the Kullback-Leibler divergence. Under this approach, the efficient market hypothesis is modelled by means of the maximum entropy RNP. This methodology consists of three steps: firstly simulating a finite number of market states of some underlying stochastic model, secondly choosing a set of assets—called benchmarks—with characteristics close to the given one, and thirdly calculating an RNP by means of the minimization of its divergence from the maximum entropy distribution over the simulated finite sample market states, i.e. from the uniform distribution. This maximum entropy RNP must exactly price the benchmarks by their quoted prices. Here we proceed in a different way consisting of the minimization of a different divergence resulting in the total variation distance. This is done by means of a two steps linear goal programming method. The calculation of the super-replicating portfolios (not supplied by the Kullback-Leibler approach) would then be derived as solutions of the dual linear programs.Item Risk neutral valuation and linear programming(2014) Vilar Zanón, José Luis; Peraita Ezcurra, OliviaGracias a la programación Lineal por metas podemos construir un método inverso para la valoración de activos.