The Formation of Financial Bubbles in Defaultable Markets

Biagini, Francesca and Nedelcu, Sorin (2015): The Formation of Financial Bubbles in Defaultable Markets. In: SIAM Journal on Financial Mathematics, Vol. 6, No. 1: pp. 530-558

Abstract

In this paper we study the formation of financial bubbles in the valuation of defaultable claims in a reduced-form setting. The birth of a bubble is caused by the impact of trading activity of investors, who consider the claim to be a safe investment under some circumstances. We also show how microeconomic interactions may, at an aggregate level, determine a shift in the martingale measure. In this way we establish a connection between our approach and the martingale theory of bubbles; see [F. Biagini, H. Föllmer, and S. Nedelcu, Finance Stoch., 18 (2014), pp. 297--326] and [R. Jarrow, P. Protter, and K. Shimbo, Math. Finance, 20 (2010), pp. 145--185]. This is illustrated by a characterization of the space of equivalent local martingale measures by measure pasting. Furthermore, our model is consistent with the no-arbitrage framework, as we show in a concrete example.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1945-497X
• Language: English