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15
MICROSTRUCTURE NOISE, REALIZED VARIANCE, AND OPTIMAL SAMPLING
, 2005
"... Observed asset prices are known to deviate from their efficient values due to market microstructure frictions. This paper studies the effects of market microstructure noise on nonparametric estimates of the efficient price integrated variance. Specifically, we consider both asymptotic and finite sam ..."
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Cited by 49 (5 self)
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Observed asset prices are known to deviate from their efficient values due to market microstructure frictions. This paper studies the effects of market microstructure noise on nonparametric estimates of the efficient price integrated variance. Specifically, we consider both asymptotic and finite sample effects of general market microstructure noise on realized variance estimates. The finite sample results culminate in a variance/bias tradeoff that serves as a basis for an optimal sampling theory. Our theory also considers the effects of prefiltering the data and proposes a novel biascorrection. We show that this theory is easily implementable in practise requiring only the calculation of sample moments of the observable highfrequency return data.
Stochastic integration in UMD Banach spaces
 Ann. Probab
"... Abstract. In this paper we construct a theory of stochastic integration of processes with values in L(H, E), where H is a separable Hilbert space and E is a UMD Banach space. The integrator is an Hcylindrical Brownian motion. Our approach is based on a twosided L pdecoupling inequality for UMD sp ..."
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Cited by 6 (3 self)
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Abstract. In this paper we construct a theory of stochastic integration of processes with values in L(H, E), where H is a separable Hilbert space and E is a UMD Banach space. The integrator is an Hcylindrical Brownian motion. Our approach is based on a twosided L pdecoupling inequality for UMD spaces due to Garling, which is combined with the theory of stochastic integration of L(H, E)valued functions introduced recently by two of the authors. We obtain various characterizations of the stochastic integral and prove versions of the Itô isometry, the BurkholderDavisGundy inequalities, and the representation theorem for Brownian martingales. 1.
Strict local martingales, bubbles, and no early exercise
, 2007
"... We show pathological behavior of asset price processes modeled by continuous strict local martingales under a riskneutral measure. The inspiration comes from recent results on financial bubbles. We analyze, in particular, the effect of the strict nature of the local martingale on the usual formula ..."
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Cited by 5 (0 self)
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We show pathological behavior of asset price processes modeled by continuous strict local martingales under a riskneutral measure. The inspiration comes from recent results on financial bubbles. We analyze, in particular, the effect of the strict nature of the local martingale on the usual formula for the price of a European call option, especially a strong anomaly when call prices decay monotonically with maturity. A complete and detailed analysis for the archetypical strict local martingale, the reciprocal of a three dimensional Bessel process, has been provided. Our main tool is based on a general htransform technique (due to Delbaen and Schachermayer) to generate positive strict local martingales. This gives the basis for a statistical test to verify a suspected bubble is indeed one (or not).
Specification Tests For The Variance Of A Diffusion
, 1998
"... We propose specification tests for the variance of a diffusion that do not require complete knowledge of the functional form under the null. We first propose a test for the constancy of the variance that, under the null of constancy, has a limiting normal distribution, while under the alternative of ..."
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Cited by 4 (0 self)
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We propose specification tests for the variance of a diffusion that do not require complete knowledge of the functional form under the null. We first propose a test for the constancy of the variance that, under the null of constancy, has a limiting normal distribution, while under the alternative of either unconditional or conditional heteroskedasticity, diverges at an appropriate rate. We then propose a test for the null of a parametric specification against the alternative of a more general func tional form. Under the null, the test has a well defined limiting distribution, normal in the unconditional and mixed normal in the conditional heteroskedasticity case; under the alternative, it diverges.
Volatility or microstructure noise?
, 2003
"... The notion of realized volatility as a modelfree measurement of the quadratic variation of the underlying log price process loses its asymptotic validity in the presence of market microstructure noise. Should microstructure contaminations be present, the summing of an increasing number of squared r ..."
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Cited by 1 (0 self)
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The notion of realized volatility as a modelfree measurement of the quadratic variation of the underlying log price process loses its asymptotic validity in the presence of market microstructure noise. Should microstructure contaminations be present, the summing of an increasing number of squared return data (as in the definition of the realized volatility estimator) simply entails increasing accumulation of noise. Using asymptotic arguments as in the extant theoretical literature on the subject, we show that the realized volatility estimator diverges to infinity almost surely when noise plays a role as in a realistic price formation mechanism. We also show that, while the quadratic variation of the log price process cannot be estimated consistently, an appropriately standardized version of the realized volatility estimator can be employed to uncover a specific feature of the noise distribution, namely the second moment of the noise process. 1 1
unknown title
, 2005
"... www.elsevier.com/locate/spa Duality formula for the bridges of a Brownian diffusion: Application to gradient drifts Sylvie Roelly a,,1, Miche ` le Thieullen b ..."
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www.elsevier.com/locate/spa Duality formula for the bridges of a Brownian diffusion: Application to gradient drifts Sylvie Roelly a,,1, Miche ` le Thieullen b
and mathematical finance the early years,
"... The history of stochastic integration and the modelling of risky asset prices both begin with Brownian motion, so let us begin there too. The earliest attempts to model Brownian motion mathematically can be traced to three sources, each of which knew nothing about the others: the first was that of T ..."
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The history of stochastic integration and the modelling of risky asset prices both begin with Brownian motion, so let us begin there too. The earliest attempts to model Brownian motion mathematically can be traced to three sources, each of which knew nothing about the others: the first was that of T. N. Thiele of Copenhagen, who effectively created a model of Brownian motion while studying time series in 1880 [80]. 1; the second was that of L. Bachelier of Paris, who created a model of Brownian motion while deriving the dynamic behavior of the Paris stock market, in 1900 (see, [1, 2, 11]); and the third was that of A. Einstein, who proposed a model of the motion of small particles suspended in a liquid, in an attempt to convince other physicists of the molecular nature of matter, in 1905 [21](See [63] for a discussion of Einstein’s model and his motivations.) Of these three models, those of Thiele and Bachelier had little impact for a long time, while that of Einstein was immediately influential. We go into a little detail about what happened to Bachelier, since he is now seen by many as the founder of modern Mathematical Finance. Ignorant of the
Forward and Futures Prices with Bubbles
, 2008
"... This paper extends and re…nes the Jarrow, Protter, Shimbo [12], [13] arbitrage free pricing theory for bubbles to characterize forward and futures prices. Some new insights are obtained in this regard. In particular, we: (i) provide a canonical process for asset price bubbles suitable for empirical ..."
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This paper extends and re…nes the Jarrow, Protter, Shimbo [12], [13] arbitrage free pricing theory for bubbles to characterize forward and futures prices. Some new insights are obtained in this regard. In particular, we: (i) provide a canonical process for asset price bubbles suitable for empirical estimation, (ii) discuss new methods to test empirically for asset price bubbles using both spot prices and call/put option prices on the spot commodity, (iii) show that futures prices always equal their fundamental values, (iv) relate forward and futures prices under bubbles, and (v) price options on futures with asset price bubbles.
unknown title
, 2006
"... On random measures, unordered sums and discontinuities of the first kind ..."