TY - JOUR

T1 - Evaluating hedging errors

T2 - An asymptotic approach

AU - Hayashi, Takaki

AU - Mykland, Per A.

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2005/4

Y1 - 2005/4

N2 - We propose a methodology for evaluating the hedging errors of derivative securities due to the discreteness of trading times or the observation times of market prices, or both. Utilizing a weak convergence approach, we derive the asymptotic distributions of the hedging errors as the discreteness disappears in several situations. First, we examine the hedging error due to discrete-time trading when the true strategy is known, which generalizes the result of Bertsimas, Kogan, and Lo (2000) to continuous Itô processes. Then we consider a data-driven strategy, when the true strategy is unknown. This strategy is free of parametric model assumptions, therefore it is expected to serve as a benchmark for the evaluation of parametric strategies. Finally, we consider a case study of the Black-Scholes delta-hedging strategy when the volatility is unknown in the proposed framework. The results obtained give us a prospect for further developments of the framework under which various parametric strategies could be compared in a unified manner.

AB - We propose a methodology for evaluating the hedging errors of derivative securities due to the discreteness of trading times or the observation times of market prices, or both. Utilizing a weak convergence approach, we derive the asymptotic distributions of the hedging errors as the discreteness disappears in several situations. First, we examine the hedging error due to discrete-time trading when the true strategy is known, which generalizes the result of Bertsimas, Kogan, and Lo (2000) to continuous Itô processes. Then we consider a data-driven strategy, when the true strategy is unknown. This strategy is free of parametric model assumptions, therefore it is expected to serve as a benchmark for the evaluation of parametric strategies. Finally, we consider a case study of the Black-Scholes delta-hedging strategy when the volatility is unknown in the proposed framework. The results obtained give us a prospect for further developments of the framework under which various parametric strategies could be compared in a unified manner.

KW - Delta hedging

KW - Incomplete market

KW - Model uncertainty

KW - Nonparametric regression

KW - Weak convergence

UR - http://www.scopus.com/inward/record.url?scp=17444363812&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17444363812&partnerID=8YFLogxK

U2 - 10.1111/j.0960-1627.2005.00221.x

DO - 10.1111/j.0960-1627.2005.00221.x

M3 - Article

AN - SCOPUS:17444363812

VL - 15

SP - 309

EP - 343

JO - Mathematical Finance

JF - Mathematical Finance

SN - 0960-1627

IS - 2

ER -