Nonparametric estimation for i.i.d. paths of a martingale-driven model with application to non-autonomous financial models

Nicolas Marie ()
Additional contact information
Nicolas Marie: Université Paris Nanterre

Finance and Stochastics, 2023, vol. 27, issue 1, No 3, 97-126

Abstract: Abstract This paper deals with a projection least squares estimator of the function J 0 $J_{0}$ computed from multiple independent observations on [ 0 , T ] $[0,T]$ of the process Z $Z$ defined by d Z t = J 0 ( t ) d 〈 M 〉 t + d M t $dZ_{t} = J_{0}(t)d\langle M\rangle _{t} + dM_{t}$ , where M $M$ is a continuous square-integrable martingale vanishing at 0. Risk bounds are established for this estimator, an associated adaptive estimator and an associated discrete-time version used in practice. An appropriate transformation allows us to rewrite the differential equation d X t = V ( X t ) ( b 0 ( t ) d t + σ ( t ) d B t ) $dX_{t} = V(X_{t})(b_{0}(t)dt +\sigma (t)dB_{t})$ , where B $B$ is a fractional Brownian motion with Hurst parameter H ∈ [ 1 / 2 , 1 ) $H\in [1/2,1)$ , as a model of the previous type. The second part of the paper deals with risk bounds for a nonparametric estimator of b 0 $b_{0}$ derived from the results on the projection least squares estimator of J 0 $J_{0}$ . In particular, our results apply to the estimation of the drift function in a non-autonomous Black–Scholes model and to nonparametric estimation in a non-autonomous fractional stochastic volatility model.

Keywords: Projection least squares estimator; Model selection; Fractional Brownian motion; Stochastic differential equations; Stochastic volatility; 60H10; 60H30; 62G05 (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00780-022-00493-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:finsto:v:27:y:2023:i:1:d:10.1007_s00780-022-00493-8

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

DOI: 10.1007/s00780-022-00493-8

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().