Pricing with Variance Gamma Information

Lane P. Hughston and Leandro Sánchez-Betancourt

Chapter 16 in Financial Informatics:An Information-Based Approach to Asset Pricing, 2022, pp 371-392 from World Scientific Publishing Co. Pte. Ltd.

Abstract: In the information-based pricing framework of Brody, Hughston & Macrina, the market filtration {ℱt}t≥0 is generated by an information process {ℱt}t≥0 defined in such a way that at some fixed time T an ℱt-measurable random variable XT is “revealed”. A cash flow Ht is taken to depend on the market factor Xt, and one considers the valuation of a financial asset that delivers Ht at time T. The value of the asset St at any time t ∊ [0, T) is the discounted conditional expectation of Ht with respect to ℱt, where the expectation is under the risk neutral measure and the interest rate is constant. Then ST− = Ht, and St = 0 for t ≥ T. In the general situation one has a countable number of cash flows, and each cash flow can depend on a vector of market factors, each associated with an information process. In the present work we introduce a new process, which we call the normalized variance-gamma bridge. We show that the normalized variance-gamma bridge and the associated gamma bridge are jointly Markovian. From these processes, together with the specification of a market factor Xt, we construct a so-called variance-gamma information process. The filtration is then taken to be generated by the information process together with the gamma bridge. We show that the resulting extended information process has the Markov property and hence can be used to develop pricing models for a variety of different financial assets, several examples of which are discussed in detail.

Keywords: Financial Mathematics; Mathematical Finance; Financial Markets; Informatics; Asset Pricing; Asset Price Dynamics; Stochastic Modelling; Information Process; Information Flow; Signal Processing; Filtration; Brownian Motion; Brownian Bridge; Change of Measure; Stochastic Volatility; Credit Risk; Default; Equities; Bonds; Collateralized Debt Obligation; Discount Bond; Lévy Process; Lévy Random Bridge; Lévy Information; Gamma Bridge; Markov Bridge; Pricing Kernel; Option Pricing; Informed Traders; Insurance; Reinsurance; Insurance Claims; Bond Portfolio; Heat Kernel; Markov Process; Variance Gamma Process; Ornstein-Uhlenbeck Process; Commodities; Fake News (search for similar items in EconPapers)
JEL-codes: C02 C6 G12 (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.worldscientific.com/doi/pdf/10.1142/9789811246494_0016 (application/pdf)
https://www.worldscientific.com/doi/abs/10.1142/9789811246494_0016 (text/html)
Ebook Access is available upon purchase.

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:wsi:wschap:9789811246494_0016

Ordering information: This item can be ordered from

Access Statistics for this chapter

More chapters in World Scientific Book Chapters from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().