Relative Asset Price Bubbles

Bilina-Falafala, Roseline; Jarrow, Robert A.; Protter, Philip

doi:10.2139/ssrn.2265465

Cited by 3 publications

(1 citation statement)

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“…Note that the payoff of the defaultable claim (and the corresponding wealth process associated to the claim) must not be not upper bounded, since the martingale theory of financial bubbles does not allow for bubbles in the price of bounded asset prices. A possible way of avoiding this limitation is by introducing the concept of a relative asset price bubble, see Bilina Falafala, Jarrow, and Protter [5].…”

Section: Bubbles In Defaultable Claim Valuationmentioning

confidence: 99%

The Formation of Financial Bubbles in Defaultable Markets

Biagini

Nedelcu

2015

SIAM J. Finan. Math.

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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.

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Section: Bubbles In Defaultable Claim Valuationmentioning

confidence: 99%

The Formation of Financial Bubbles in Defaultable Markets

Biagini

Nedelcu

2015

SIAM J. Finan. Math.

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Shifting martingale measures and the birth of a bubble as a submartingale

2013

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Detecting asset price bubbles using deep learning

Biagini,

Gonon,

Mazzon

et al. 2024

Mathematical Finance

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In this paper, we employ deep learning techniques to detect financial asset bubbles by using observed call option prices. The proposed algorithm is widely applicable and model‐independent. We test the accuracy of our methodology in numerical experiments within a wide range of models and apply it to market data of tech stocks in order to assess if asset price bubbles are present. Under a given condition on the pricing of call options under asset price bubbles, we are able to provide a theoretical foundation of our approach for positive and continuous stochastic asset price processes. When such a condition is not satisfied, we focus on local volatility models. To this purpose, we give a new necessary and sufficient condition for a process with time‐dependent local volatility function to be a strict local martingale.

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Relative Asset Price Bubbles

Cited by 3 publications

References 45 publications

The Formation of Financial Bubbles in Defaultable Markets

The Formation of Financial Bubbles in Defaultable Markets

Shifting martingale measures and the birth of a bubble as a submartingale

Detecting asset price bubbles using deep learning

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