Modeling and pricing of variance and volatility swaps for local semi-Markov volatilities in financial engineering
type: Item
instance of: scholarly article
title: Modeling and pricing of variance and volatility swaps for local semi-Markov volatilities in financial engineering
zbMATH Open document ID: 1202.91355
DOI: 10.1155/2010/537571
author: Anatoliy Swishchuk
author: Raimondo Manca
published in: Mathematical Problems in Engineering
publication date: 2010-12-23T00:00:00Z
full work available at URL: https://eudml.org/doc/228952
review text: Summary: 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.
Mathematics Subject Classification ID: 91G80
Mathematics Subject Classification ID: 91G30
Mathematics Subject Classification ID: 91G20
zbMATH DE Number: 5829233
MaRDI profile type: Publication
OpenAlex ID: W2076237346
Wikidata QID: Q58653143
cites work: Q4794126
cites work: Q3108077
cites work: The pricing of options and corporate liabilities
cites work: Option pricing: A simplified approach
cites work: Q4863379
cites work: Q4905685
cites work: Q3374309
cites work: A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
cites work: Pricing Options and Variance Swaps in Markov-Modulated Brownian Markets
cites work: Q4507774
cites work: Q5423050
cites work: Generalized autoregressive conditional heteroscedasticity
cites work: Q4220653
cites work: Complete Models with Stochastic Volatility
cites work: Mathematical Finance
cites work: Q4320114
cites work: Q5529437
cites work: Valuing credit default swap in a non-homogeneous semi-Markovian rating based model
description: scientific article; zbMATH DE number 5829233