A Comparison between the Pricing of Capped and Power Options on the Basis of Arbitrage Prevention: Evidence from a Stochastic Market with Double Stochastic Volatility, Double Jump, and a Stochastic Intensity Measure

Abstract

Objective: In this paper, three types of power options under special stochastic markets have been priced. In the considered market, a risky underlying asset follows a model with two stochastic volatilities, two jumps, and a stochastic intensity measure. Generally, a power option is supposed to generate more income and benefit than other options. There exist, nevertheless, some methods thwarting the opportunities and one of these methods is considering a barrier such as a cap for power option income. The aim of this study is to draw a comparison between the ability of capped and power options in generating arbitrage opportunities. Method: In this study capped and power options are compared in order to find probable arbitrage opportunities under the considered market. For this purpose, comparisons are made on the basis of a hypothetical condition, applying the Tehran Stock Exchange index as an underlying asset. Then, the profits of these two options extracted from the data of the Tehran Stock Exchange have been compared. Results: Our findings indicate that between the capped and power options, the former has a higher ability to handicap the profit of arbitrage opportunities.

Keywords

• power option
• capped option
• fast fourier transform
• stochastic volatility
• stochastic intensity