VALUATION OF EUROPEAN PUT OPTION BY USING THE QUADRATURE METHOD UNDER THE VARIANCE GAMMA PROCESS

Authors

  • Akash Singh Research Scholar, Department of Mathematics, Gujarat University, India
  • Ravi Gor Department of Mathematics, Gujarat University, India
  • Rinku Patel P.G. student, Department of Mathematics, Gujarat University, India

DOI:

https://doi.org/10.29121/ijoest.v4.i4.2020.101

Keywords:

Variance Gamma Process, Quadrature Method, European Put Option, Geometric Brownian Motion

Abstract

Dynamic asset pricing model uses the Geometric Brownian Motion process. The Black-Scholes model known as standard model to price European option based on the assumption that underlying asset prices dynamic follows that log returns of asset is normally distributed. In this paper, we introduce a new stochastic process called levy process for pricing options. In this paper, we use the quadrature method to solve a numerical example for pricing options in the Indian context. The illustrations used in this paper for pricing the European style option.  We also try to develop the pricing formula for European put option by using put-call parity and check its relevancy on actual market data and observe some underlying phenomenon.

Downloads

Download data is not yet available.

References

Andricopoulos, A. D., Widdicks, M., Duck, P. W., & Newton, D. P. (2003). Universal option valuation using quadrature methods. Journal of Financial Economics, 67(3), 447-471.

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.

Sullivan, M. A. (2000). Valuing American put options using Gaussian quadrature. The Review of Financial Studies, 13(1), 75-94.

Geske, R., & Torous, W. (1991). Skewness, kurtosis, and black-scholes option mispricing. Statistical Papers, 32(1), 299.

Madan, D. B., & Seneta, E. (1990). The variance gamma (VG) model for share market returns. Journal of business, 511-524.

Cont, R., & Tankov, P. (2004). Nonparametric calibration of jump-diffusion option pricing models.

Lindner, A., & Sato, K. I. (2011). Properties of stationary distributions of a sequence of generalized Ornstein–Uhlenbeck processes. Mathematische Nachrichten, 284(17‐18), 2225-2248.

Permana, F. J. (2014). Valuation of European and American Options under Variance Gamma Process. Journal of Applied Mathematics and Physics, 2(11), 1000.

Ivanovski, Z., Stojanovski, T., & Narasanov, Z. (2015). Volatility and kurtosis of daily stock returns at MSE. UTMS Journal of Economics, 6(2), 209-221.

Madan, D. B., & Milne, F. (1991). Option pricing with vg martingale components 1. Mathematical finance, 1(4), 39-55.

Downloads

Published

2020-09-23

How to Cite

Singh, A., Gor, R. G., & Patel, R. . (2020). VALUATION OF EUROPEAN PUT OPTION BY USING THE QUADRATURE METHOD UNDER THE VARIANCE GAMMA PROCESS. International Journal of Engineering Science Technologies, 4(5), 1–5. https://doi.org/10.29121/ijoest.v4.i4.2020.101