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Grasping the historical volatility of stock market indices and accurately estimating are two of the major focuses of those involved in the financial securities industry and derivative instruments pricing. This paper presents the results of…
The goals of this paper are twofold: (1) to present a new method that is able to find linear laws governing the time evolution of Markov chains and (2) to apply this method for anomaly detection in Bitcoin prices. To accomplish these goals,…
We consider the hedging problem where a futures position can be automatically liquidated by the exchange without notice. We derive a semi-closed form for an optimal hedging strategy with dual objectives - to minimise both the variance of…
A model is proposed for Bitcoin prices that takes into account market attention. Market attention, modeled by a mean-reverting Cox-Ingersoll-Ross processes, affects the volatility of Bitcoin returns, with some delay. The model is affine and…
In this paper, we explore some stylized facts of the Bitcoin market using the BTC-USD exchange rate time series of historical intraday data from 2013 to 2020. Bitcoin presents some very peculiar idiosyncrasies, like the absence of…
We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be…
Bitcoin constructs temporal order internally rather than synchronizing to any external clock. Empirical evidence shows that its time evolution is non-continuous, probabilistic, and self-regulated. Block discovery follows a stochastic…
A Levy-driven Ornstein-Uhlenbeck process is proposed to model the evolution of the risk-free rate and default intensities for the purpose of evaluating option contracts on a credit index. Time evolution in credit markets is assumed to…
In quantitative finance, we often model asset prices as a noisy Ito semimartingale. As this model is not identifiable, approximating by a time-changed Levy process can be useful for generative modelling. We give a new estimate of the…
We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finite dimensional Gaussian process (GP)…
This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed…
The bitcoin price has surged in recent years and it has also exhibited phases of rapid decay. In this paper we address the question to what extent this novel cryptocurrency market can be viewed as a classic or semi-efficient market. Novel…
The usage of a spot volatility estimate based on a volatility decomposition in a time-changed price-model according to the trading times is investigated. In this model clock-time volatility splits up into the product of tick-time volatility…
In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call…
The CBOE Volatility Index, known by its ticker symbol VIX, is a popular measure of the market's expected volatility on the SP 500 Index, calculated and published by the Chicago Board Options Exchange (CBOE). It is also often referred to as…
We consider discrete time models for asset prices with a stationary volatility process. We aim at estimating the multivariate density of this process at a set of consecutive time instants. A Fourier type deconvolution kernel density…
Using 1-min returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed, and kurtosis largely deviates from the Gaussian…
The paper constructs a multi-variate Hawkes process model of Bitcoin block arrivals and price jumps. Hawkes processes are selfexciting point processes that can capture the self- and cross-excitation effects of block mining and Bitcoin price…
Volatility of financial stock is referring to the degree of uncertainty or risk embedded within a stock's dynamics. Such risk has been received huge amounts of attention from diverse financial researchers. By following the concept of…
How do supply and demand from informed traders drive market prices of bitcoin options? Deribit options tick-level data supports the limits-to-arbitrage hypothesis about the market maker's supply. The main demand-side effects are that…