Allende, H., Elias, C., & Torres, S. (2004). Estimation of the option prime: Microsimulation of backward stochastic differential equations. Int. Stat. Rev., 72(1), 107–121.
Abstract: A mathematical statistical model is needed to obtain an option prime and create a hedging strategy. With formulas derived from stochastic differential equations, the primes for US Dollar/Chilean Pesos currency options using a prime calculator are obtained. Furthermore, a backward simulation of the option prime trajectory is used with a numerical method created for backward stochastic differential equations. The use of statistics in finance is highly important in order to develop complex products.

Araya, H., Bahamonde, N., Fermin, L., Roa, T., & Torres, S. (2023). ON THE CONSISTENCY OF LEAST SQUARES ESTIMATOR IN MODELS SAMPLED AT RANDOM TIMES DRIVEN BY LONG MEMORY NOISE: THE JITTERED CASE. Stat. Sin., 33(1), 331–351.
Abstract: In numerous applications, data are observed at random times. Our main purpose is to study a model observed at random times that incorporates a longmemory noise process with a fractional Brownian Hurst exponent H. We propose a least squares estimator in a linear regression model with longmemory noise and a random sampling time called “jittered sampling”. Specifically, there is a fixed sampling rate 1/N, contaminated by an additive noise (the jitter) and governed by a probability density function supported in [0, 1/N]. The strong consistency of the estimator is established, with a convergence rate depending on N and the Hurst exponent. A Monte Carlo analysis supports the relevance of the theory and produces additional insights, with several levels of longrange dependence (varying the Hurst index) and two different jitter densities.

Araya, H., Bahamonde, N., Fermin, L., Roa, T., & Torres, S. (2023). ON THE CONSISTENCY OF THE LEAST SQUARES ESTIMATOR IN MODELS SAMPLED AT RANDOM TIMES DRIVEN BY LONG MEMORY NOISE: THE RENEWAL CASE. Stat. Sin., 33(1), 1–26.
Abstract: In this study, we prove the strong consistency of the least squares estimator in a random sampled linear regression model with longmemory noise and an independent set of random times given by renewal process sampling. Additionally, we illustrate how to work with a random number of observations up to time T = 1. A simulation study is provided to illustrate the behavior of the different terms, as well as the performance of the estimator under various values of the Hurst parameter H.
