A parsimonious model for generating arbitrage-free scenario trees

Angelo Carollo, Andrea Consiglio, Stavros A. Zenios

Research output: Contribution to journalArticle

14 Citations (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.
Original languageEnglish
Pages (from-to)201-212
Number of pages12
JournalQuantitative Finance
Volume16
Publication statusPublished - 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

Cite this

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

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

Research output: Contribution to journalArticle

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