Finance and Stochastics

, Volume 20, Issue 3, pp 589–634

Additive subordination and its applications in finance

Article

DOI: 10.1007/s00780-016-0300-8

Cite this article as:
Li, J., Li, L. & Mendoza-Arriaga, R. Finance Stoch (2016) 20: 589. doi:10.1007/s00780-016-0300-8

Abstract

This paper studies additive subordination, which we show is a useful technique for constructing time-inhomogeneous Markov processes with analytical tractability. This technique is a natural generalization of Bochner’s subordination that has proved to be extremely useful in financial modeling. Probabilistically, Bochner’s subordination corresponds to a stochastic time change with respect to an independent Lévy subordinator, while in additive subordination, the Lévy subordinator is replaced by an additive one. We generalize the classical Phillips theorem for Bochner’s subordination to the additive subordination case, based on which we provide Markov and semimartingale characterizations for a rich class of jump-diffusions and pure jump processes obtained from diffusions through additive subordination, and obtain spectral decomposition for them. To illustrate the usefulness of additive subordination, we develop an analytically tractable cross-commodity model for spread option valuation that is able to calibrate the implied volatility surface of each commodity. Moreover, our model can generate implied correlation patterns that are consistent with market observations and economic intuitions.

Keywords

Bochner’s subordination Additive subordination Time-inhomogeneous Markov processes Spread options 

Mathematics Subject Classification

47D06 47D07 60J35 60J60 60J75 91G20 

JEL Classification

G13 

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.CITIC SecuritiesBeijingChina
  2. 2.Department of Systems Engineering and Engineering ManagementThe Chinese University of Hong KongShatinHong Kong
  3. 3.Department of Information, Risk and Operations Management, McCombs School of BusinessThe University of Texas at AustinAustinUSA

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