Solution of a Model for Pricing Options with Hedging Strategy Through Nonlinear Filters

Luis Sánchez, P. Freddy Sánchez, A. Freddy Sánchez, Norma Bargary

Research output: Contribution to journalArticlepeer-review

Abstract

A methodology is presented to estimate the solution states for a non-linear price problem, a model for pricing options with a hedging strategy in the Föllmer-Schweizer sense is defined. The problem is to determine the price of a contingent claim, that is a contract, that pays of an amount at time t in a incomplete market, that is not possible to replicate a payoff by a controlled portfolio of the basic securities. Two algorithms are presented to estimate the solution of the presented problem, the nested sequential Monte Carlo (NSMC) and space-time particle filter (STPF) are defined from sequences of probability distributions. The methodology is validated to use real data from option Asian, the states in real-time are estimated, that is proposed on the basis of the price model. The efficiency of the forecasts of the model is compared. Finally, one goodness-of-fit measure to validate the performance of the model are used, obtaining insignificant estimation error.

Original languageEnglish
Pages (from-to)34-44
Number of pages11
JournalStatistics, Optimization and Information Computing
Volume12
Issue number1
DOIs
Publication statusPublished - Jan 2024

Keywords

  • Hedging strategy
  • Nested sequential Monte Carlo
  • Non-linear price problems
  • Space-time particle filter
  • Stochastic Differential Equation

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