Pricing Options and Variance Swaps in Markov-Modulated Brownian Markets

Robert J. Elliott () and Anatoliy V. Swishchuk ()
Additional contact information
Robert J. Elliott: University of Calgary
Anatoliy V. Swishchuk: University of Calgary

Chapter 4 in Hidden Markov Models in Finance, 2007, pp 45-68 from Springer

Abstract: Summary A Markov-modulated market consists of a riskless asset or bond, B, and a risky asset or stock, S, whose dynamics depend on Markov process x. We study the pricing of options and variance swaps in such markets. Using the martingale characterization of Markov processes, we note the incompleteness of Markov-modulated markets and find the minimal martingale measure. Black-Scholes formulae for Markov-modulated markets with or without jumps are derived. Perfect hedging in a Markov-modulated Brownian and a fractional Brownian market is not possible as the market is incomplete. Following the idea proposed by Föllmer and Sondermann [13] and Föllmer and Schweizer [12]) we look for the strategy which locally minimizes the risk. The residual risk processes are determined in these situations. Variance swaps for stochastic volatility driven by Markov process are also studied.

Keywords: Markov-modulated markets with jumps; option pricing; variance swaps; minimal martingale measure (search for similar items in EconPapers)
Date: 2007
References: Add references at CitEc
Citations: View citations in EconPapers (9)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-0-387-71163-8_4

Ordering information: This item can be ordered from
http://www.springer.com/9780387711638

DOI: 10.1007/0-387-71163-5_4

Access Statistics for this chapter

More chapters in International Series in Operations Research & Management Science from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().