JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Option Pricing with Bounded Expected Loss under Variance-Gamma Processes
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Option Pricing with Bounded Expected Loss under Variance-Gamma Processes
Song, Seong-Joo; Song, Jong-Woo;
  PDF(new window)
 Abstract
Exponential Levy models have become popular in modeling price processes recently in mathematical finance. Although it is a relatively simple extension of the geometric Brownian motion, it makes the market incomplete so that the option price is not uniquely determined. As a trial to find an appropriate price for an option, we suppose a situation where a hedger wants to initially invest as little as possible, but wants to have the expected squared loss at the end not exceeding a certain constant. For this, we assume that the underlying price process follows a variance-gamma model and it converges to a geometric Brownian motion as its quadratic variation converges to a constant. In the limit, we use the mean-variance approach to find the asymptotic minimum investment with the expected squared loss bounded. Some numerical results are also provided.
 Keywords
Option pricing;variance-gamma processes;weak convergence;incomplete market;bounded loss;
 Language
English
 Cited by
 References
1.
Andersen, P. K., Borgen, O., Gill, R. D. and Keiding, N. (1992). Statistical Models Based on Counting Processes, Springer-Verlag, New York.

2.
Barndorff-Nielsen, O. E. (1998). Processes of normal inverse Gaussian type, Finance and Stochastics, 2, 41-68. crossref(new window)

3.
Carr, P., Geman, H., Madan, D. B. and Yor, M. (2002). The fine structure of asset returns: An empirical investigation, Journal of Business, 75, 305-332. crossref(new window)

4.
Cont, R. and Tankov, P. (2004). Financial Modelling with Jump Processes, Chapman & Hall/CRC.

5.
Eberlein, E. and Keller, U. (1995). Hyperbolic distributions in Finance, Bernoulli, 1, 281-299. crossref(new window)

6.
Geman, H. (2002). Pure jump Levy processes for asset price modelling, Journal of Banking and Finance, 21, 755-763.

7.
Hong, D. and Wee, I. (2003). Convergence of Jump-Diffusion models to the Black-Scholes model, Stochastic Analysis and Applications, 21, 141-160. crossref(new window)

8.
Jacod, J. and Shiryaev, A. N. (1987). Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin.

9.
Kurtz, T. G. and Protter, P. E. (1991). Weak limit theorems for stochastic integrals and stochastic differential equations, Annals of Probability, 19, 1035-1070. crossref(new window)

10.
Madan, D. B. and Seneta, E. (1990). The VG model for share market returns, Journal of Business, 63, 511-524. crossref(new window)

11.
Schoutens, W. (2003). Levy Processes in Finance: Pricing Financial Derivatives, Wiley.

12.
Song, S. and Mykland, P. A. (2006). An asymptotic decomposition of hedging errors, Journal of the Korean Statistical Society, 35, 115-142.

13.
Song, S. and Song, J. (2008). Asymptotic option price with bounded expected loss, Journal of the Korean Statistical Society, 37, 323-334. crossref(new window)