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271 results · page 8 of 12
InĂ©s JimĂ©nez, AndrĂ©s MoraâValencia, Javier Perote
No abstract is available for this record.
Abootaleb Shirvani, Stefan Mittnik, W. Brent Lindquist, Svetlozar T. Rachev
We propose a doubly subordinated Levy process, NDIG, to model the time series properties of the cryptocurrency bitcoin. NDIG captures the skew and fat-tailed properties of bitcoin prices and gives rise to an arbitrage free, option pricing model. In this framework we derive two bitcoin volatility measures. The first combines NDIG option pricing with the Cboe VIX model to compute an implied volatility; the second uses the volatility of the unit time increment of the NDIG model. Both are compared to a volatility based upon historical standard deviation. With appropriate linear scaling, the NDIG process perfectly captures observed, in-sample, volatility.
Zhenghong Qiu, Jianhui Huang, Tinghan Xie
This paper investigates a class of unified stochastic linear-quadratic-Gaussian (LQG) social optima problems involving a large number of weakly-coupled interactive agents under a generalized setting. For each individual agent, the control and state process enters both diffusion and drift terms in its linear dynamics, and the control weight might be indefinite in cost functional. This setup is innovative and has great theoretical and realistic significance as its applications in mathematical finance (e.g., portfolio selection in mean-variation model). Using some fully-coupled variational analysis under the person-by-person optimality principle, and the mean-field approximation method, the decentralized social control is derived by a class of new type consistency condition (CC) system for typical representative agent. Such CC system is some mean-field forward-backward stochastic differential equation (MF-FBSDE) combined with embedding representation. The well-posedness of such forward-backward stochastic differential equation (FBSDE) system is carefully examined. The related social asymptotic optimality is related to the convergence of the average of a series of weakly-coupled backward stochastic differential equation (BSDE). They are verified through some Lyapunov equations.
Sabrı Burak Arzova, Caner Ăzdurak
We apply the Markowitz mean-variance framework to assess risk-return benefits of cryptocurrency-portfolios. Using daily data of the three major cryptocurrencies for the time span 1/1/2019 to 27/04/2021, we relate risk and return of different mean-variance portfolio strategies to Bitcoin, Etherium, Ripple and BIST 30 benchmark. We find that combining cryptocurrencies crowds out BIST 30 index to maximize return and Sharpe ratio while cryptocurrencies are crowded out if the optimization problem is changed to a risk minimization problem rather than a return maximization problem. Furthermore, according to rolling-window approach shift from Bitcoin to Etherium is important.
Alvaro Guinea, Alet Roux
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 tractable, with closed formulae for the conditional characteristic functions with respect to both the conventional and a delayed filtration. This leads to semi-closed formulae for European call and put prices. A maximum likelihood estimation procedure is provided, as well as a method for changing to a risk-neutral measure. The model compares very well against classical and attention-based models when tested on real data.
Pierre Venter, Eben Maré
In this paper, the HestonâNandi futures option pricing model is applied to Bitcoin futures options. The model prices are compared to market prices to give an indication of the pricing performance. In addition, a multivariate Bitcoin futures option pricing methodology based on a multivatiate GARCH model is developed. The empirical results show that a symmetric model is a better fit when applied to Bitcoin futures returns, and also produces more accurate option prices compared to market prices for two out of three expiry dates considered.
Melanie Cao, Batur Celik
Abstract We propose an equilibrium valuation model for bitcoin options by extending Cao. Bitcoin is interpreted as a foreign currency in a small open economy where money supply and aggregate dividend are exogenous. The equilibrium bitcoin prices increase with diffusive and jump risks of these two exogenous factors. Analytical option pricing formulas are obtained with Merton's model as a special case. Static analysis reveals that a bitcoin call (put) option value increases (decreases) with the money supply growth rate. Numerical analysis shows that all risks lead to a positive premium in option prices relative to the BlackâScholes model.
Julian Winkel
Unter Verwendung eines neuen Datensatzes von Deribit, einer der gröĂten Bitcoin Derivate Börsen, werden Bitcoin Pricing Kernel berechnet. Diese ermöglichen die arbitragefreie Bepreisung neuer Instrumente. State Price Densities werden mit Rookleys Methode geschĂ€tzt. Der zugrundeliegende Bitcoin Asset Prozess wird als ein SVCJ Modell betrachtet. Die geschĂ€tzten Pricing Kernel werden in einem forminvarianten Kernel zusammengefasst. Mit der Struktur der Pricing Kernel werden Marktineffizienzen gefunden, denen mit einer simulierten Handelsstrategie entgegengewirkt werden kann.
Zini Wang, Guangxin Jiang, Qiang Ye
Abstract Cryptocurrency is one of the earliest and the most successful applications of blockchain, and it utilizes the distributed ledger, which is a commonly used technique in blockchain, to make a decentralized transaction within the blockchain of a cryptocurrency. However, how to make a decentralized transaction of cryptocurrencies between parties on different blockchains, that is, the crossâchain exchange, is not wellâstudied. In this paper, we develop a new method to make crossâchain exchanges based on the classical atomic swap. We first study the optionality embedded into the atomic swap and propose to add a premium into the atomic swap, and then design a new procedure with the premium to guarantee the fairness of the crossâchain exchange. We also provide an algorithm based on the leastâsquares Monte Carlo method to estimate the premium and analyze the convergence of the algorithm. Moreover, we study the crossâchain exchange with margin trading. We propose an adapted exchange procedure to make a fair crossâchain exchange and an algorithm to estimate the fair premium under the margin trading. Numerical experiments are provided to show the effectiveness of the algorithms.
Sang Hoon Kang
This paper investigates the long memory property of four cryptocurrencies (Bitcoin, Dash, Ethereum, and Litecoin) using the Rescaled Range Hurst analysis. The presence of long memory test for the validity of efficient market hypothesis in the cryptocurrency markets. First, we use traditional long memory tests (Hurst-Mandelbrot R/S, GSP and GPH) to investigate the long memory property in the returns and volatilities of cryptocurrency markets. We find that the volatility shows strong long memory property. Second, we employs the rolling sample approach and calculate time-varying long memory propertty in the returns and volatilities of cryptocurrency markets. Emprical results show that both the volatility and returns of cryptocurrency markets possess the time-varying long memory property. The average Hurst exponents are well above 0.5, indicating the presence of long memory. The long memory property of volatility is stronger than that of returns. The time-varying Hurst exponent values for BTC are significant higher than those of other cryptocurrencies (DASH, ETH, and LTC). This finding indicates that BTC is less efficient than other cryptocurrency markets. Therefore, the presence of long memory is important to predict future cryptocurrency prices, for asset allocation, and for portfolio assessment.
Claude Rodrigue Bambe Moutsinga, Edson Pindza, Eben Maré
No abstract is available for this record.
JingâZhi Huang, Zhijian Huang, Li Xu
This paper studies the dynamics of cryptocurrency volatility using a stochastic volatility model with simultaneous and correlated jumps in returns and volatility. We estimate the model using an efficient sequential learning algorithm that allows for learning about multiple unknown model parameters simultaneously, with daily data on four popular cryptocurrencies. We find that these cryptocurrencies have quite different volatility dynamics. In particular, they exhibit different return-volatility relationships: While Ethereum and Litecoin show a negative relationship, Chainlink displays a positive one and interestingly, Bitcoinâs one changes from negative to positive in June 2016. We also provide evidence that the sequential learning algorithm helps better detect large jumps in the cryptocurrency market in real time. Overall, incorporating volatility jumps helps better capture the dynamic behavior of highly volatile cryptocurrencies.
Lin William Cong, George Andrew Karolyi, Ke Tang, Weiyi Zhao
No abstract is available for this record.
Weihao Han, David Newton, Emmanouil Platanakis, Charles Sutcliffe · 5 authors
Cryptocurrency returns are highly non-normal, casting doubt on the standard performance metrics. We apply almost stochastic dominance (ASD), which does not require any assumption about the return distribution or degree of risk aversion. From 29 long-short cryptocurrency factor portfolios, we find eight that dominate our four benchmarks. Their returns cannot be fully explained by the three-factor coin model of Liu et al. (2022). So we develop a new three-factor model where momentum is replaced by a mispricing factor based on size and risk-adjusted momentum, which significantly improves pricing performance.
Mesias Alfeus, Shiam Kannan
In the current paper, we develop a methodology to price lookback options for cryptocurrencies. We propose a discretely monitored window average lookback option, whose monitoring frequencies are randomly selected within the time to maturity, and whose monitoring price is the average asset price in a specified window surrounding the instant. We price these options whose underlying asset is the CCI30 index of various Cryptocurrencies, as opposed to a single cryptocurrency, with the intention of reducing volatility, and thus, the option price. We employ the Normal Inverse Gaussian (NIG) and Rough Fractional Stochastic Volatility (RFSV) models to the cryptocurrency market and using the Black-Scholes as the benchmark model. In doing so, we intend to capture the extreme characteristics such as jumps and volatility roughness for cryptocurrency price fluctuations. Since there is no availability of a closed-form solution for lookback option prices under these models, we utilize the Monte Carlo simulation for pricing and augment it using the antithetic method for variance reduction. Finally, we present the simulation results for the lookback options and compare the prices resulting from using the NIG model, RFSV model with those from the Black-Scholes model. We found that the option price is indeed lower for our proposed window average lookback option than for a traditional lookback option. We found the Hurst parameter to be H = 0.09 which confirms that the cryptocurrencies market is indeed rough.
Vincent Danos, Hamza El Khalloufi, Julien Prat
No abstract is available for this record.
Ndeye Fatou Sene, Mamadou Abdoulaye Konté, Jane Aduda
The objective of this study is, to show the importance of incorporating jumps in both returns and volatility dynamics for Bitcoin. For that purpose, we introduce the Double Exponential Jump-Diffusion model with Stochastic Volatility (DEJDSVJ) that contains asymmetric jumps. The use of the Markov Chain Monte Carlo methods for estimation has proved the meaningful presence of jumps in Bitcoin price and volatility. Moreover, based on the Bitcoin options market, a comparison between the underlying model, the Double Exponential Jump Diffusion model (DEJD) with Stochastic Volatility (no Jumps) and the Stochastic Volatility (SV) shows the goodness of the DEJDSVJ modelâs calibration over others for pricing Bitcoin options.
Ilias Filippou, David E. Rapach, Christoffer Thimsen
No abstract is available for this record.
Yizhou Cao, Min Dai, Steven Kou, Lewei Li · 5 authors
Abstract Existing cryptocurrencies are too volatile to be used as currencies for daily payments. Stablecoins, which are cryptocurrencies pegged to other stable financial assets such as the US dollar, are desirable for payments within blockchain networks, whereby being often called the âHoly Grail of cryptocurrency.â By using the option pricing theory and the Ethereum platform that allows running smart contracts, we design several dualâclass structures that are written on the ETH cryptocurrency and offer a fixedâincome crypto asset (Class A coin), a stablecoin (Class AâČ coin) pegged to a traditional currency, and leveraged investment instruments (Class B and BâČ coins). Our investigation of the values of stablecoins in the presence of jump risk and black swanâtype events shows the robustness of the design. The design has been implemented on the Ethereum platform.
Yosef Bonaparte
No abstract is available for this record.
Zehua Zhang, Ran Zhao
No abstract is available for this record.
Lili Matic, Natalie Packham, Wolfgang Karl HĂ€rdle
The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study the hedge behaviour and effectiveness for the class of affine jump diffusion models and infinite activity Levy processes. First, market data is calibrated to stochastic volatility inspired (SVI)-implied volatility surfaces to price options. To cover a wide range of market dynamics, we generate Monte Carlo price paths using an SVCJ model (stochastic volatility with correlated jumps), a close-to-actual-market GARCH-filtered kernel density estimation as well as a historical backtest. In all three settings, options are dynamically hedged with Delta, Delta-Gamma, Delta-Vega and Minimum Variance strategies. Including a wide range of market models allows to understand the trade-off in the hedge performance between complete, but overly parsimonious models, and more complex, but incomplete models. The calibration results reveal a strong indication for stochastic volatility, low jump frequency and evidence of infinite activity. Short-dated options are less sensitive to volatility or Gamma hedges. For longer-dated options, tail risk is consistently reduced by multiple-instrument hedges, in particular by employing complete market models with stochastic volatility.
Morishige Takane
Diese Masterarbeit greift die Theorie der Portfoliooptimierung auf: die mathematische Formulierung des Problems, seine Ableitungen (Risikominimierungsformulierung) und Annahmen, seine EinschrÀnkungen sowie einige Verbesserungen und Erweiterungen des bestehenden Frameworks. Ziel der Arbeit ist es auch, in Python zu simulieren und zu implementieren: Markowitz (Global Varianzminimal, Maximum Sharpe), Hierarchical Risk Parity und drei naiv Portfolios: gleichgewichtete, inverse VolatilitÀt und inverse Varianz in der neuartigen Anlageklasse der KryptowÀhrungen. Als Benchmark wird die CRyptocurrency IndeX, CRIX, verwendet. Die Portfoliooptimierung wird anhand von 120 Tagen tÀglicher historischer Daten berechnet, wobei die Portfolio-Anpassung alle 7 Tage und 30 Tage erfolgt. Portfolios sind Long-Short Strategien ohne Hebelwirkung und Verbesserungen in der Kovarianzmatrix werden mithilfe von Eigenwert-Clipping der Zufallsmatrixtheorie angewendet.
InĂ©s JimĂ©nez, AndrĂ©s MoraâValencia, TrinoâManuel ĂĂguez, Javier Perote
The semi-nonparametric (SNP) modeling of the return distribution has been proved to be a flexible and accurate methodology for portfolio risk management that allows two-step estimation of the dynamic conditional correlation (DCC) matrix. For this SNP-DCC model, we propose a stepwise procedure to compute pairwise conditional correlations under bivariate marginal SNP distributions, overcoming the curse of dimensionality. The procedure is compared to the assumption of Dynamic Equicorrelation (DECO), which is a parsimonious model when correlations among the assets are not significantly different but requires joint estimation of the multivariate SNP model. The risk assessment of both methodologies is tested for a portfolio on cryptocurrencies by implementing backtesting techniques and for different risk measures: Value-at-Risk, Expected Shortfall and Median Shortfall. The results support our proposal showing that the SNP-DCC model has better performance for a smaller confidence level than the SNP-DECO model, although both models perform similarly for higher confidence levels.