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

Akash Singh,Rinku Patel,Ravi Gor Gor

doi:10.29121/ijoest.v4.i4.2020.101

Akash Singh, Rinku Patel + Show 1 more

Open Access

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

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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.

Highlights

In option pricing theory the main problem is to find the fair value of an option
Black-Scholes model is based on the assumption that the underlying asset price observes the Geometric Brownian motion where the log returns of the asset price is normally distributed
Madan and Seneta (1990) [5] in their theses derived The Variance Gamma (VG) model for share market returns which is based on levy process

Summary

INTRODUCTION

In option pricing theory the main problem is to find the fair value of an option. To find the value of European option a well-known model named Black-Scholes model which is based on certain assumptions. Black-Scholes model is based on the assumption that the underlying asset price observes the Geometric Brownian motion where the log returns of the asset price is normally distributed. Valuation of European Put Option by Using the Quadrature Method Under the Variance Gamma Process. Madan and Seneta (1990) [5] in their theses derived The Variance Gamma (VG) model for share market returns which is based on levy process. Ivanovski et al (2015) [9] conclude that the Geometric Brownian motion breaks to catch the characteristics feature of asset price dynamics that reveal heavy tails and excessive kurtosis. The contribution of this article is to check the relevancy of Indian context and observe some underlying phenomenon

QUADRATURE METHOD

VARIANCE GAMMA MODEL

CONCLUSION