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Paolo Guasoni - One of the best experts on this subject based on the ideXlab platform.

Miklós Rásonyi - One of the best experts on this subject based on the ideXlab platform.

Robert A Jarrow - One of the best experts on this subject based on the ideXlab platform.

  • testing the Local Martingale theory of bubbles using cryptocurrencies
    Social Science Research Network, 2020
    Co-Authors: Soon Hyeok Choi, Robert A Jarrow
    Abstract:

    Cryptocurrencies provide the ideal and natural experimental setting to test the Local Martingale theory of bubbles, because they have no cash flows. Using this theory, we test for the existence of price bubbles in eight cryptocurrencies from January 1, 2019 to July 17, 2019. The cryptocurrencies are Bitcoin (BTC), Litecoin (LTC), Ethereum (ETH), Ripple (XRP), Bitcoin Cash (BCH), EOS (EOS), Monero (XMR), and Zcash (ZEC). A novel, simple, and robust testing methodology is created to facilitate this estimation. During this time frame, five of the eight currencies (BTC, BCH, EOS, XMR, ZEC) exhibit price bubbles, Litecoin does not, and the evidence for Ethereum and Ripple is inconclusive. The paper provides strong evidence for the prevalence of bubbles in cryptocurrencies and supports the feasibility of applying the Local Martingale theory of bubbles to various asset classes.

  • informational efficiency under short sale constraints
    Social Science Research Network, 2013
    Co-Authors: Robert A Jarrow, Martin Larsson
    Abstract:

    A constrained informationally efficient market is defined to be one whose price process arises as the outcome of some equilibrium where agents face restrictions on trade. This paper investigates the case of short sale constraints, a setting which despite its simplicity, generates new insights. In particular, it is shown that short sale constrained informationally efficient markets always admit equivalent superMartingale measures and Local Martingale deflators, but not necessarily Local Martingale measures. And if in addition some Local Martingale deflator turns the price process into a true Martingale, then the market is informationally efficient. Examples are given to illustrate the subtle phenomena that can arise in the presence of short sale constraints, with particular attention to representative agent equilibria and the different notions of no arbitrage.

  • asset price bubbles in incomplete markets
    Social Science Research Network, 2007
    Co-Authors: Robert A Jarrow, Philip Protter, Kazuhiro Shimbo
    Abstract:

    This paper studies asset price bubbles in a continuous time model using the Local Martingale framework. Providing careful definitions of the asset's market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the "no free lunch with vanishing risk (NFLVR)" and "no dominance" assumptions. We show that the two leading models for bubbles as either charges or as strict Local Martingales, respectively, are equivalent. We propose a new theory for bubble birth which involves a nontrivial modification of the classical Martingale pricing framework. This modification involves the market exhibiting different Local Martingale measures across time - a possibility not previously explored within the classical theory. Finally, we investigate the pricing of derivative securities in the presence of asset price bubbles, and we show that: (i) European put options can have no bubbles, (ii) European call options and discounted forward prices have bubbles whose magnitudes are related to the asset's price bubble, (iii) with no dividends, American call options may be exercised early, (iv) European put-call parity in market prices must always hold, regardless of bubbles, and (v) futures price bubbles can exist and they are independent of the underlying asset's price bubble. Many of these results stand in contrast to those of the classical theory. We propose, but do not implement, some new tests for the existence of asset price bubbles using derivative securities.

Hao Xing - One of the best experts on this subject based on the ideXlab platform.

Shiqi Song - One of the best experts on this subject based on the ideXlab platform.

  • No arbitrage of the first kind and Local Martingale numéraires
    Finance and Stochastics, 2016
    Co-Authors: Yuri Kabanov, Constantinos Kardaras, Shiqi Song
    Abstract:

    A superMartingale deflator (resp. Local Martingale deflator) multiplicatively transforms nonnegative wealth processes into superMartingales (resp. Local Martingales). A superMartingale numeraire (resp. Local Martingale numeraire) is a wealth process whose reciprocal is a superMartingale deflator (resp. Local Martingale deflator). It has been established in previous works that absence of arbitrage of the first kind (\(\mbox{NA}_{1}\)) is equivalent to the existence of the (unique) superMartingale numeraire, and further equivalent to the existence of a strictly positive Local Martingale deflator; however, under \(\mbox{NA}_{1}\), a Local Martingale numeraire may fail to exist. In this work, we establish that under \(\mbox{NA}_{1}\), a superMartingale numeraire under the original probability \(P\) becomes a Local Martingale numeraire for equivalent probabilities arbitrarily close to \(P\) in the total variation distance.

  • Local Martingale deflators for asset processes stopped at a default time s tau or right before s tau
    Research Papers in Economics, 2016
    Co-Authors: Shiqi Song
    Abstract:

    Let $\mathbb{F}\subset \mathbb{G}$ be two filtrations and $S$ be a $\mathbb{F}$ semiMartingale possessing a $\mathbb{F}$ Local Martingale deflator. Consider $\tau$ a $\mathbb{G}$ stopping time. We study the problem whether $S^{\tau-}$ or $S^{\tau}$ can have $\mathbb{G}$ Local Martingale deflators. A suitable theoretical framework is set up in this paper, within which necessary/sufficient conditions for the problem to be solved have been proved. Under these conditions, we will construct $\mathbb{G}$ Local Martingale deflators for $S^{\tau-}$ or for $S^{\tau}$. Among others, it is proved that $\mathbb{G}$ Local Martingale deflators are multiples of $\mathbb{F}$ Local Martingale deflators, with a multiplicator coming from the multiplicative decomposition of the Az\'ema superMartingale of $\tau$. The proofs of the necessary/sufficient conditions require various results to be established about Az\'ema superMartingale, about Local Martingale deflator, about filtration enlargement, which are interesting in themselves. Our study is based on a filtration enlargement setting. For applications, it is important to have a method to infer the existence of such setting from the knowledge of the market information. This question is discussed at the end of the paper.

  • No arbitrage and Local Martingale deflators
    arXiv: Probability, 2015
    Co-Authors: Yuri Kabanov, Constantinos Kardaras, Shiqi Song
    Abstract:

    A superMartingale deflator (resp., Local Martingale deflator) multiplicatively transforms nonnegative wealth processes into superMartingales (resp., Local Martingales). The superMartingale numeraire (resp., Local Martingale numeraire) is the wealth processes whose reciprocal is a superMartingale deflator (resp., Local Martingale deflator). It has been established in previous literature that absence of arbitrage of the first kind (NA1) is equivalent to existence of the superMartingale numeraire, and further equivalent to existence of a strictly positive Local Martingale deflator; however, under NA1, the Local Martingale numeraire may fail to exist. In this work, we establish that, under NA1, any total-variation neighbourhood of the original probability has an equivalent probability under which the Local Martingale numeraire exists. This result, available previously only for single risky-asset models, is in striking resemblance with the fact that any total-variation neighbourhood of a separating measure contains an equivalent $\sigma$-Martingale measure. The presentation of our main result is relatively self-contained, including a proof of existence of the superMartingale numeraire under NA1. We further show that, if the Levy measures of the asset-price process have finite support, NA1 is equivalent to existence of the Local Martingale numeraire with respect to the original probability.

  • Local Martingale deflators for asset processes stopped at a default time s mathfrak t or just before s mathfrak t
    2014
    Co-Authors: Shiqi Song
    Abstract:

    Let $\mathbb{F}\subset \mathbb{G}$ be two filtrations and $S$ be a $\mathbb{F}$ semiMartingale possessing a $\mathbb{F}$ Local Martingale deflator. Consider $\tau$ a $\mathbb{G}$ stopping time. We study the problem whether $S^{\tau-}$ or $S^{\tau}$ can have $\mathbb{G}$ Local Martingale deflators. A suitable theoretical framework is set up in this paper, within which necessary/sufficient conditions for the problem to be solved have been proved. Under these conditions, we will construct $\mathbb{G}$ Local Martingale deflators for $S^{\tau-}$ or for $S^{\tau}$. Among others, it is proved that $\mathbb{G}$ Local Martingale deflators are multiples of $\mathbb{F}$ Local Martingale deflators, with a multiplicator coming from the multiplicative decomposition of the Azema superMartingale of $\tau$. The proofs of the necessary/sufficient conditions require various results to be established about Azema superMartingale, about Local Martingale deflator, about filtration enlargement, which are interesting in themselves. Our study is based on a filtration enlargement setting. For applications, it is important to have a method to infer the existence of such setting from the knowledge of the market information. This question is discussed at the end of the paper.

  • an explicit model of default time with given survival probability
    Stochastic Processes and their Applications, 2011
    Co-Authors: Monique Jeanblanc, Shiqi Song
    Abstract:

    For a given filtered probability space , an -adapted continuous increasing process [Lambda] and a positive - Local Martingale N such that [Lambda]0=0 and Nte-[Lambda]t