Additive subordination and its applications in finance

Jing Li (), Lingfei Li () and Rafael Mendoza-Arriaga ()
Additional contact information
Jing Li: CITIC Securities
Lingfei Li: The Chinese University of Hong Kong
Rafael Mendoza-Arriaga: The University of Texas at Austin

Finance and Stochastics, 2016, vol. 20, issue 3, No 2, 589-634

Abstract: 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; 47D06; 47D07; 60J35; 60J60; 60J75; 91G20 (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s00780-016-0300-8

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