Related papers: Empirical forward price distribution from Bitcoin …
In recent years, cryptocurrencies have attracted growing attention from both private investors and institutions. Among them, Bitcoin stands out for its impressive volatility and widespread influence. This paper explores the predictability…
The distribution of the returns for a stock are not well described by a normal probability density function (pdf). Student's t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of…
We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a…
This paper measures price differences between Hegic option quotes on Arbitrum and a model-based benchmark built on Black--Scholes model with regime-sensitive volatility estimated via a two-regime MS-AR-(GJR)-GARCH model. Using option-level…
Bitcoin's price has been described as following a power law (PL) in time, $P \sim t^{\beta}$ with $\hat\beta \approx 5.7$ over 2010-2026. We test this claim using the Clauset-Shalizi-Newman protocol applied to Bitcoin's tail-relevant…
Cryptocurrencies, especially Bitcoin (BTC), which comprise a new digital asset class, have drawn extraordinary worldwide attention. The characteristics of the cryptocurrency/BTC include a high level of speculation, extreme volatility and…
The aim of this paper is to analyse the Bitcoin in order to shed some light on its nature and behaviour. We select 9 cryptocurrencies that account for almost 75\% of total market capitalisation and compare their evolution with that of a…
In this paper, we discuss the method of Bayesian regression and its efficacy for predicting price variation of Bitcoin, a recently popularized virtual, cryptographic currency. Bayesian regression refers to utilizing empirical data as proxy…
To cope with the negative oil futures price caused by the COVID-19 recession, global commodity futures exchanges temporarily switched the option model from Black--Scholes to Bachelier in 2020. This study reviews the literature on…
Financial time series have historically been assumed to be a martingale process under the Random Walk hypothesis. Instead of making investment decisions using the raw prices alone, various multimodal pattern matching algorithms have been…
We analyze the time series of overnight returns for the bund and btp futures exchanged at LIFFE (London). The overnight returns of both assets are mapped onto a one-dimensional symbolic-dynamics random walk: The `bond walk'. During the…
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the…
In this paper we study the pricing of exchange options when underlying assets have stochastic volatility and stochastic correlation. An approximation using a closed-form approximation based on a Taylor expansion of the conditional price is…
We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random…
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…
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…
This paper examines the relationship between Inverse Perpetual Swap contracts, a Bitcoin derivative akin to futures and the margin funding interest rates levied on BitMEX. This paper proves the Heteroskedastic nature of funding rates and…
We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied…
We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017--2020, we model…
Introduction: The paper addresses the challenging problem of predicting the short-term realized volatility of the Bitcoin price using order flow information. The inherent stochastic nature and anti-persistence of price pose difficulties in…