The Formation of Financial Bubbles in Defaultable Markets

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 [2] and [27]. 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.

Asset Price Bubbles in market models with proportional transaction costs

“…Another approach defines the fundamental value of an asset by its super-replication prices, see [28], [29]. Other approaches explain in a mathematical model the impact of microeconomic interactions on asset price formation, see [10], [36]. In [36], the fundamental value is exogenously given and asset price bubbles are endogenously determined by the impact of liquidity risk.…”

“…In [36], the fundamental value is exogenously given and asset price bubbles are endogenously determined by the impact of liquidity risk. In [10], microeconomic dynamics may at an aggregate level determine a shift in the martingale measure. Further references on asset price bubbles are [7], [8], [9], [30], [34], [35], [52].…”

A risk-neutral equilibrium leading to uncertain volatility pricing

“…A related work is [11], where the Föllmer measure is used to construct a pricing operator that restores put-call-parity for complete models where the exchange rate is driven by a strict local martingale. Further examples include [7], where bubbles in defaultable claims are studied, and [6,17], who focus on the interplay between bubbles and insider information as well as model uncertainty, respectively. Surveys of this large and growing literature can be found in [33,52].…”

Liquidity Induced Asset Bubbles via Flows of ELMMs

“…On the other hand, an alternative model is given by Jarrow, Protter and Roch in [28], where the fundamental value is exogenously given, whereas the market value is endogenously determined by the trading activity of investors, and studied through the analysis of the liquidity supply curve. For another constructive model, see also [9]. In this setting a bubble is still defined as the difference between the market value W and the fundamental value W F , however it does not always coincide with the Q-bubble under a given equivalent martingale measure Q.…”