Modeling and Pricing of Variance and Volatility Swaps for Local Semi-Markov Volatilities in Financial Engineering. (18th October 2010)

• Record Type: Journal Article
• Authors: Swishchuk, Anatoliy; Manca, Raimondo
• Other Names: Rega G. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2010(2010)
• Publication Date: 2010-10-18
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2010/537571
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We consider a semi-Markov modulated security market consisting of a riskless asset or bond with constant interest rate and risky asset or stock, whose dynamics follow gemoetric Brownian motion with volatility that depends on semi-Markov process. Two cases for semi-Markov volatilities are studied: local current and local semi-Markov volatilities. Using the martingale characterization of semi-Markov processes, we find the minimal martingale measure for this incomplete market. Then we model and price variance and volatility swaps for local semi-Markov stochastic volatilities.