TY - JOUR
T1 - Solution of a Model for Pricing Options with Hedging Strategy Through Nonlinear Filters
AU - Sánchez, Luis
AU - Sánchez, P. Freddy
AU - Sánchez, A. Freddy
AU - Bargary, Norma
N1 - Publisher Copyright:
© 2024 International Academic Press
PY - 2024/1
Y1 - 2024/1
N2 - 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.
AB - 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.
KW - Hedging strategy
KW - Nested sequential Monte Carlo
KW - Non-linear price problems
KW - Space-time particle filter
KW - Stochastic Differential Equation
UR - http://www.scopus.com/inward/record.url?scp=85178237311&partnerID=8YFLogxK
U2 - 10.19139/soic-2310-5070-1626
DO - 10.19139/soic-2310-5070-1626
M3 - Article
AN - SCOPUS:85178237311
SN - 2311-004X
VL - 12
SP - 34
EP - 44
JO - Statistics, Optimization and Information Computing
JF - Statistics, Optimization and Information Computing
IS - 1
ER -