Related papers: Scaling Limits for Super--replication with Transie…
Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…
We investigate the probability distribution of the volatility return intervals $\tau$ for the Chinese stock market. We rescale both the probability distribution $P_{q}(\tau)$ and the volatility return intervals $\tau$ as…
We study portfolio selection in a complete continuous-time market where the preference is dictated by the rank-dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the…
We study Vanna-Volga methods which are used to price first generation exotic options in the Foreign Exchange market. They are based on a rescaling of the correction to the Black-Scholes price through the so-called `probability of survival'…
Investors always want to know about the profit and the risk that they will be get before buying some assets. Our main focus is getting the profit and the probability of getting that profit using the differential evolution algorithm for…
We model the logarithm of the price (log-price) of a financial asset as a random variable obtained by projecting an operator stable random vector with a scaling index matrix $\underline{\underline{E}}$ onto a non-random vector. The scaling…
The key objective of this paper is to develop an empirical model for pricing SPX options that can be simulated over future paths of the SPX. To accomplish this, we formulate and rigorously evaluate several statistical models, including…
In this paper we derive a second order approximation for an infinite dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator…
We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that…
The irreducible decomposition of successive restriction and induction of irreducible representations of a symmetric group gives rise to a Markov chain on Young diagrams keeping the Plancherel measure invariant. Starting from this Res-Ind…
Traders and investors involved in an option contract having the underlying stock in range bound are likely to lose their initial investment. Timing in buying an option contract is of capital importance. In a recent article [1] the…
We analyze the complexity of Gibbs samplers for inference in crossed random effect models used in modern analysis of variance. We demonstrate that for certain designs the plain vanilla Gibbs sampler is not scalable, in the sense that its…
Extreme events can come either from point processes, when the size or energy of the events is above a certain threshold, or from time series, when the intensity of a signal surpasses a threshold value. We are particularly concerned by the…
The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is…
We consider several aspects of the scaling limit of percolation on random planar triangulations, both finite and infinite. The equivalents for random maps of Cardy's formula for the limit under scaling of various crossing probabilities are…
Detection of power-law behavior and studies of scaling exponents uncover the characteristics of complexity in many real world phenomena. The complexity of financial markets has always presented challenging issues and provided interesting…
In this paper we present a method for obtaining tail-bounds for random variables satisfying certain probabilistic recurrences that arise in the analysis of randomized parallel divide and conquer algorithms. In such algorithms, some…
We establish general sufficient conditions for a sequence of controlled branching processes to converge weakly on the Skorokhod space. We focus on a class of controlled random variables that extends previous results by considering them as a…
In this work we introduce the notion of fully incomplete markets. We prove that for these markets the super-replication price coincide with the model free super-replication price. Namely, the knowledge of the model does not reduce the…
This paper studies the problem of trading futures with transaction costs when the underlying spot price is mean-reverting. Specifically, we model the spot dynamics by the Ornstein-Uhlenbeck (OU), Cox-Ingersoll-Ross (CIR), or exponential…