Consider the sum Y=B+B^H of a Brownian motion B and an independent fractional Brownian motion B^H with Hurst parameter H ∈ (0,1). Surprisingly, even though B^H is not a semimartingale, Cheridito proved in that Y is a semimartingale if H3/4. Moreover, Y is locally equivalent to B in this case,...

In this paper, we present a stochastic optimal control model to optimize an insurance firm problem in the case where its cash-balance process is assumed to be described by a stochastic differential equation driven by Teugels martingales. Noticing that the insurance firm is able to control its...

We complete the investigation on the asymptotic behavior of the drift burst test statistic devised in Christensen, Oomen and Ren\`o (2020). They analysed it for an Ito semimartingale containing a Brownian component and finite variation jumps. We also account for infinite variation jumps.We show...

In view of their tractability, Hawkes processes are widely employed in high-frequency data. However, even in the absence of kernel (i.e. Poisson case), it is well-documented empirically that the baseline is not constant, reproducing in particular seasonalities from the financial market. In this...

This research article provides criticism and arguments why the canonical framework for derivatives pricing is incomplete and why the delta-hedging approach is not appropriate. An argument is put forward, based on the efficient market hypothesis, why a proper risk-adjusted discount rate should...

This paper studies efficient market hypothesis in prediction markets and the results are illustrated for the in-play football betting market using the quoted odds for the English Premier League. Our analysis is based on the martingale property, where the last quoted probability should be the...

We consider the problem of estimating volatility based on high-frequency data when the observed price process is a continuous Itô semimartingale contaminated by microstructure noise. Assuming that the noise process is compatible across different sampling frequencies, we argue that it typically...

We present a new theory for the conduct of nonparametric inference about the latent spot volatility of a semimartingale asset price process. In contrast to existing theories based on the asymptotic notion of an increasing number of observations in local estimation blocks, our theory treats the...

Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style of an option price is constructed as a difference of the certainty equivalents to the value functions solving the system of HJB equations. We introduce the...

Much of the theoretical basis for current monetary and financial theory rests on the economic efficiency of financial markets. Not surprisingly, considerable effort has been expended to test the efficient markets hypothesis, usually by examination of the predictability of equity returns....

We solve for the first time (*) a longstanding puzzle of quantitative finance that has often been described as the Holy Grail of volatility modeling: build a model that jointly and exactly calibrates to the prices of S&P 500 (SPX) options, VIX futures, and VIX options. So far the best attempts,...

Implied volatility is at the very core of modern finance, notwithstanding standard option pricing models continue to derive option prices starting from the joint dynamics of the underlying asset price and the spot volatility. These models often cause difficulties: no closed formulas for prices,...

We present an approach to analyze learning outcomes in a broad class of misspecified environments, spanning both single-agent and social learning. We introduce a novel “prediction accuracy” order over subjective models, and observe that this makes it possible to partially restore standard...

In [2], and [13], financial models based on the Wick product, and White Noise formalism are suggested. Although the original purpose is to incorporate integrals with respect to fractional Brownian motion, it is also pointed out in these articles, that this leads naturally to a quantum mechanical...

We explore simple finite sample adjustments to simulated spot FX rates, zero bonds, forward IBORs and the numeraire to ensure the martingale asset pricing property of linear IR and FX products holds exactly with a finite number of Monte Carlo simulations. The impact on CVA, DVA, and CVA-DVA...

Rough volatility models have recently been empirically shown to provide a good fit to historical volatility time series and implied volatility smiles of SPX options. They are continuous-time stochastic volatility models, whose volatility process is driven by a fractional Brownian motion with...

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...

We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment of real-valued and complex-valued semimartingales. The...

This study examines whether the Asia – Pacific Foreign Exchange Market was in a weak form of efficiency against USD, during the period from 02/01/2010 to 31/12/2019. This study employed various linear measures, to examine the martingale behaviour of Asia – Pacific Foreign Exchange Market....

This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability spaces. We establish a “broken exponential martingale” expansion that generalizes and unifies the exponentiation result of Alòs, Gatheral, and Radoičić ́ (SSRN'17; [AGR20])...

We study the influence of information about call option prices on model-independent price bounds for exotic derivatives obtained through martingale transport. The considered call option prices and their associated marginal distributions do not correspond to some future maturity on which the...

We propose an Adjusted Quasi-Score (AQS) method for constructing tests for homoskedasticity in spatial econometric models. We first obtain an AQS function by adjusting the score-type function from the given model to achieve unbiasedness, and then develop an Outer-Product-of-Martingale-Difference...

Violation of the efficient market hypothesis (EMH) in a specific market may lead to construction of bubbles which is a signal of inefficiencies. Although speculative bubbles soon decay, if they exist for a long time, they will lead to financial crises. Early warning systems (EWSs) are designed...

We study dynamic optimal portfolio allocation for monotone mean-variance preferences in a general semimartingale model. Armed with new results in this area we revisit the work of Cui, Li, Wang and Zhu (2012, MAFI) and fully characterize the circumstances under which one can set aside a...

Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung-Box tests...

In this Element the authors review the technique of the change of numeraire in the martingale approach to option pricing. Their intention is to present a reader friendly explanation of the technique itself, and illustrate how it is applied in various fields of quantitative finance as the basis...