Rate of convergence of the price of European option on a market for which the jump of stock price is uniformly distributed over an interval

• Published in: Ukrainian mathematical journal Vol. 60; no. 8; pp. 1254 - 1269
• Main Authors: Mishura, Yu. S., Soloveiko, O. M.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-08-2008
• Subjects: Algebra; Analysis; Applications of Mathematics; Geometry; Mathematics; Mathematics and Statistics; Statistics; Martingale Measure; Fair Price; American Option; Option Price; Stock Price
• ISSN: 0041-5995; 1573-9376
• DOI: 10.1007/s11253-009-0128-x

We consider a model of market for which the jump of the stock price is uniformly distributed over a certain symmetric interval. By using the theorem on asymptotic expansions of the distribution function of the sum of independent identically distributed random variables, we determine the rate of convergence of fair prices for the European options. It is shown that, in the prelimit model, there exists a martingale measure on the market such that the rate of convergence of the prices of European options to the Black-Scholes price has an order of 1/
n
1/2
.