Pricing with Variance Gamma Information

Hughston, L P and Sánchez-Betancourt, L. 2020. Pricing with Variance Gamma Information. Risks, 8(4), 105. ISSN 2227-9091 [Article]

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Abstract or Description

In the information-based pricing framework of Brody, Hughston & Macrina, the market filtration {Ft}_t≥0 is generated by an information process {ξ_t}t≥0 defined in such a way that at some fixed time T an F_T -measurable random variable X_T is “revealed”. A cash flow H_T is taken to depend on the market factor X_T , and one considers the valuation of a financial asset that delivers H_T at T. The value of the asset S_t at any time t ∈ [0, T ) is the discounted conditional expectation of H_T with respect to F_t, where the expectation is under the risk neutral measure and the interest rate is constant. Then S_T− = H_T , and S_t = 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 X_T , 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.

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Information-based asset pricing, Lévy processes, gamma processes, variance gamma processes, Brownian bridges, gamma bridges, nonlinear filtering.

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30 September 2020Accepted
10 October 2020Published

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Date Deposited:

05 Oct 2020 10:05

Last Modified:

09 Feb 2022 14:04

Peer Reviewed:

Yes, this version has been peer-reviewed.


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