TY - JOUR

T1 - Uniform convergence of empirical characteristic functions in a complex domain with applications to option pricing

AU - Binkowski, Karol

AU - Kozek, Andrzej

PY - 2010

Y1 - 2010

N2 - In Csörgo{double acute} and Totik (1983) and Csörgo{double acute} (1985) it has been shown that in the case of independent identically distributed (iid) random variables X1, X2, ..., Xn the empirical characteristic function (ecf) over(φ{symbol}, ̂)n (u) converges uniformly, for | u | ≤ Un to the characteristic function φ{symbol} (u) of X, on increasing intervals which union covers the whole real line. We show that if suitable moments exist then the uniform convergence is also valid for u in the complex domain x = u + i ν, | u | ≤ Un, ν ∈ (a, b), where a < b depend on the cumulative distribution function F of X. This extension has an important application in Stochastic Finance in option pricing for Lévy processes. It allows us to prove the convergence of an empirical option pricing formula to the theoretical value of the option and opens a way towards option pricing based on empirical characteristic functions. Crown

AB - In Csörgo{double acute} and Totik (1983) and Csörgo{double acute} (1985) it has been shown that in the case of independent identically distributed (iid) random variables X1, X2, ..., Xn the empirical characteristic function (ecf) over(φ{symbol}, ̂)n (u) converges uniformly, for | u | ≤ Un to the characteristic function φ{symbol} (u) of X, on increasing intervals which union covers the whole real line. We show that if suitable moments exist then the uniform convergence is also valid for u in the complex domain x = u + i ν, | u | ≤ Un, ν ∈ (a, b), where a < b depend on the cumulative distribution function F of X. This extension has an important application in Stochastic Finance in option pricing for Lévy processes. It allows us to prove the convergence of an empirical option pricing formula to the theoretical value of the option and opens a way towards option pricing based on empirical characteristic functions. Crown

UR - http://www.scopus.com/inward/record.url?scp=74849140621&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2009.10.017

DO - 10.1016/j.spl.2009.10.017

M3 - Article

VL - 80

SP - 270

EP - 276

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 5-6

ER -