A parsimonious model for generating arbitrage-free scenario trees

Angelo Carollo, Andrea Consiglio, Stavros A. Zenios

Risultato della ricerca: Article

14 Citazioni (Scopus)

Abstract

Simulation models of economic, financial and business risk factors are widely used to assessrisks and support decision-making. Extensive literature on scenario generation methods aims atdescribing some underlying stochastic processes with the least number of scenarios to overcomethe ‘curse of dimensionality’.There is, however, an important requirement that is usually overlookedwhen one departs from the application domain of security pricing: the no-arbitrage condition. Weformulate a moment matching model to generate multi-factors scenario trees for stochastic optimizationsatisfying no-arbitrage restrictions with a minimal number of scenarios and without any distributionalassumptions. The resulting global optimization problem is quite general. However, it is non-convexand can grow significantly with the number of risk factors, and we develop convex lower boundingtechniques for its solution exploiting the special structure of the problem. Applications to somestandard problems from the literature show that this is a robust approach for tree generation. We useit to price a European basket option in complete and incomplete markets.
Lingua originaleEnglish
pagine (da-a)201-212
Numero di pagine12
RivistaQuantitative Finance
Volume16
Stato di pubblicazionePublished - 2016

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Scenarios
Arbitrage
Risk factors
Optimization problem
Financial risk
Complete markets
Simulation model
Economic risk
Scenario generation
Incomplete markets
No-arbitrage condition
Pricing
Decision making
Curse of dimensionality
Global optimization
Multi-factor
Basket option
No-arbitrage
Stochastic processes
Business risk

All Science Journal Classification (ASJC) codes

  • Economics, Econometrics and Finance(all)
  • Finance

Cita questo

A parsimonious model for generating arbitrage-free scenario trees. / Carollo, Angelo; Consiglio, Andrea; Zenios, Stavros A.

In: Quantitative Finance, Vol. 16, 2016, pag. 201-212.

Risultato della ricerca: Article

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