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Valuation of Asian Options-with Levy Approximation

Zhang, Qian LU and Mraovic, Aleksandra LU (2014) NEKN01 20132
Department of Economics
Abstract
Asian options are difficult to price analytically. Even though they have attracted much attention in recent years, there is still no closed-form solution available for pricing the arithmetic Asian options, because the distribution of the density function is unknown. However, various studies have attempted to solve this problem, Levy (1992) approximates the unknown density function using lognormal distribution by matching the first two moments. This paper investigates how accurate the Levy approach is by comparing values of Asian options from Levy’s approach with Monte Carlo simulations. We find that Levy’s analytic solution tends to over-estimate Asian option values when volatility is constant, but under-estimates under the scenario of... (More)
Asian options are difficult to price analytically. Even though they have attracted much attention in recent years, there is still no closed-form solution available for pricing the arithmetic Asian options, because the distribution of the density function is unknown. However, various studies have attempted to solve this problem, Levy (1992) approximates the unknown density function using lognormal distribution by matching the first two moments. This paper investigates how accurate the Levy approach is by comparing values of Asian options from Levy’s approach with Monte Carlo simulations. We find that Levy’s analytic solution tends to over-estimate Asian option values when volatility is constant, but under-estimates under the scenario of having stochastic volatility. (Less)
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author
Zhang, Qian LU and Mraovic, Aleksandra LU
supervisor
organization
course
NEKN01 20132
year
type
H1 - Master's Degree (One Year)
subject
keywords
Asian options, Monte Carlo simulation, constant volatility, stochastic volatility
language
English
id
4301159
date added to LUP
2014-02-12 09:35:36
date last changed
2014-02-12 09:35:36
@misc{4301159,
  abstract     = {Asian options are difficult to price analytically. Even though they have attracted much attention in recent years, there is still no closed-form solution available for pricing the arithmetic Asian options, because the distribution of the density function is unknown. However, various studies have attempted to solve this problem, Levy (1992) approximates the unknown density function using lognormal distribution by matching the first two moments. This paper investigates how accurate the Levy approach is by comparing values of Asian options from Levy’s approach with Monte Carlo simulations. We find that Levy’s analytic solution tends to over-estimate Asian option values when volatility is constant, but under-estimates under the scenario of having stochastic volatility.},
  author       = {Zhang, Qian and Mraovic, Aleksandra},
  keyword      = {Asian options,Monte Carlo simulation,constant volatility,stochastic volatility},
  language     = {eng},
  note         = {Student Paper},
  title        = {Valuation of Asian Options-with Levy Approximation},
  year         = {2014},
}