# The rate of convergence of option prices when general martingale discrete-time scheme approximates the Black-Scholes model

Banach Center Publications (2015)

- Volume: 104, Issue: 1, page 151-165
- ISSN: 0137-6934

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topYuliya Mishura. "The rate of convergence of option prices when general martingale discrete-time scheme approximates the Black-Scholes model." Banach Center Publications 104.1 (2015): 151-165. <http://eudml.org/doc/281800>.

@article{YuliyaMishura2015,

abstract = {We take the martingale central limit theorem that was established, together with the rate of convergence, by Liptser and Shiryaev, and adapt it to the multiplicative scheme of financial markets with discrete time that converge to the standard Black-Scholes model. The rate of convergence of put and call option prices is shown to be bounded by $n^\{-1/8\}$. To improve the rate of convergence, we suppose that the increments are independent and identically distributed (but without binomial or similar restrictions on the distribution). Under additional assumptions, in particular under the assumption that absolutely continuous component of the distribution is nonzero, we apply asymptotical expansions of distribution function and establish that the rate of convergence is $O(n^\{-1/2\})$.},

author = {Yuliya Mishura},

journal = {Banach Center Publications},

keywords = {Black-Scholes model; martingale discrete-time scheme; martingale central limit theorem; convergence rates},

language = {eng},

number = {1},

pages = {151-165},

title = {The rate of convergence of option prices when general martingale discrete-time scheme approximates the Black-Scholes model},

url = {http://eudml.org/doc/281800},

volume = {104},

year = {2015},

}

TY - JOUR

AU - Yuliya Mishura

TI - The rate of convergence of option prices when general martingale discrete-time scheme approximates the Black-Scholes model

JO - Banach Center Publications

PY - 2015

VL - 104

IS - 1

SP - 151

EP - 165

AB - We take the martingale central limit theorem that was established, together with the rate of convergence, by Liptser and Shiryaev, and adapt it to the multiplicative scheme of financial markets with discrete time that converge to the standard Black-Scholes model. The rate of convergence of put and call option prices is shown to be bounded by $n^{-1/8}$. To improve the rate of convergence, we suppose that the increments are independent and identically distributed (but without binomial or similar restrictions on the distribution). Under additional assumptions, in particular under the assumption that absolutely continuous component of the distribution is nonzero, we apply asymptotical expansions of distribution function and establish that the rate of convergence is $O(n^{-1/2})$.

LA - eng

KW - Black-Scholes model; martingale discrete-time scheme; martingale central limit theorem; convergence rates

UR - http://eudml.org/doc/281800

ER -

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