Valuation of Asian Options under Variance Gamma Process

Articles

Valuation of Asian Options under Variance Gamma Process [CET 2014]
Author(s)
Dharma Lesmono
ABSTRACT
Many options are tailored to hedge the market risk of underlying assets. Asian option, an option whose payoff depends on the average prices over a certain period, is becoming a good choice in case the underlying asset prices of options are highly volatile. The average prices can reduce the volatility so buying an Asian option can be cheaper than buying a plain vanilla option. However the geometric Brownian motion (GBM) often fails to de-scribe the dynamic of asset prices, especially when asset prices are highly volatile. The high volatility will exhibit heavy tails and its distribution will be leptokurtic. Many studies on real data in the markets shows that the Var-iance Gamma (VG) process performs much better than GBM model since parameters of such distribution can also capture the kurtosis of empirical data. Under assumption the log return of the underlying asset follows the VG gamma process, we cannot directly apply the Black Scholes and the binomial tree models to valuation of options. Here, we propose a model to value an Asian option. Our model is a modification of the path simulation model proposed by Tiley. Simulation study shows that the proposed method performs well in term of the option price.
KEYWORDS
Asian Options, Variance Gamma Process
References