Amit Chaudhary, Roman Kozhan, Ganesh Viswanath-Natraj
This paper studies determinants of interest rates on Decentralized lending protocols. Using transaction level data, we show these protocols are being used to make long or short leveraged positions in the cryptocurrency market. We identify a significant relationship between the interest rate differential and the perpetual futures premium for the ETH/USDT market. However, the link is economically weak, indicating that the speculative beliefs in the two markets are only weakly correlated and that the markets are segmented. Arbitrage across the two markets is ineffective due to wide no-arbitrage bounds, which are governed by high trading costs, gas fees, and price impacts.
We applied the SVAR-LiNGAM to illustrate the causal relationships between the spot exchange rate, and three crypto-asset exchange rates, Bitcoin, Ethereum, and Ripple. It was notable that the causal order, the EUR_USD spot rate->Bitcoin->Ethereum->Ripple, was obtained by this approach. All the instantaneous effects were strongly positive. Moreover, it was notable that Bitcoin can influence the EUR_USD spot rate positively with a one-day time lag.
Yongjing Wang, Zubair Ahmad, Faridoon Khan, Dalia Kamal Alnagar ¡ 7 authors
This paper offers the introduction of a new updated form of the Dagum distribution. The new updated form of the Dagum model is called a novel generalized-Dagum distribution. The proposed novel generalized-Dagum distribution is a prominent updated form of the Dagum model with a single additional/extra parameter. The novel generalized-Dagum model is produced by mixing the Dagum distribution with the novel generalized-M distributions approach. The heavy-tailed properties of the novel generalized-Dagum model are obtained. The derivation of the estimators and a simulation study of the novel generalized-Dagum distribution are also provided. Finally, the novel generalized-Dagum model is illustrated by analyzing two real-life data sets related to the financial sector. The first data set represents the Bitcoin exchange rates vs the United States dollars. Whereas, the second data set represents the Ethereum exchange rates vs the United States dollars. Using the Bitcoin and Ethereum exchange rates data sets, the fitting power of the novel generalized-Dagum model is compared with the transmuted Dagum distribution and a new modified Dagum distribution.
Open access
Statistical Distribution Estimation and Applications
We investigate Bitcoin pricing characteristics and find evidence of jumps and positive convenience yield. We develop a theoretical jump diffusion model for options on spots and use simulations to evaluate non-linear parameter estimates. Data from the Deribit exchange is used to compare the performance of the jump diffusion models with Practitioner BlackâScholes models. Using DieboldâMarino statistics and standard error metrics, we find that the jump diffusion models significantly outperform Practitioner BlackâScholes models. We conclude that Bitcoin behaves more like a commodity than a currency.
Mnacho Echenim, Emmanuel Gobet, Anne-Claire Maurice
We design a novel calibration procedure that is designed to handle the specific characteristics of options on cryptocurrency markets, namely large bid-ask spreads and the possibility of missing or incoherent prices in the considered data sets. We show that this calibration procedure is significantly more robust and accurate than the standard one based on trade and mid-prices.
We examine the distribution of realized Bitcoin daily log-returns and find significantly-thin tails. From there we construct a simple connection back to traditional volatility modelling. And then we discuss how this connection can serve as a foundation to leverage existing derivative quant research to explore cryptocurrency market dynamics. These results also suggest a connection between cryptocurrency exchange structure and trading dynamics.
The crypto market is growing rapidly in the post pandemic era. It is expected to grow at a rate 12% compounding per annum in the near future. There is a shift in investorsâ interest towards crypto currencies has gained greater significance, Young India investors are keen in exploring newer investment avenues such as Bitcoin, Ethereum, Polygon, etc., which can provide them diversified returns. In India more than 15 million retail investors are currently trading with these digital currencies. The present study aims at examining the volatility in the crypto currencies market with the help of GARCH family models. The most powerful currency the Bitcoin and other currencies like Ethereum and Cardano were considered as samples to understand the volatility in the markets.
Optimal simple rules for the monetary policy of the first stochastically dominant crypto-currency are derived in a Dynamic Stochastic General Equilibrium (DSGE) model, in order to provide optimal responses to changes in inflation, output, and other sources of uncertainty. The optimal monetary policy stochastically dominates all the previous crypto-currencies, thus the efficient portfolio is to go long on the stochastically dominant crypto-currency: a strategy-proof arbitrage featuring a higher Omega ratio with higher expected returns, inducing an investment-efficient Nash equilibrium over the crypto-market. Zero-knowledge proofs of the monetary policy are committed on the blockchain: an implementation is provided.
Bitcoin Pricing Kernels (PKs) are estimated using a novel data set from Deribit, the leading Bitcoin options exchange. The PKs, as the ratio between risk-neutral and physical density, dynamically reflect the change in investor preferences. Thus, the PKs improve the understanding of investor expectations and risk premiums in a new asset class. Bootstrap-based confidence bands are estimated in order to validate the results. Investors are heterogeneous in their risk profiles and preferences with respect to volatility and investment horizon. The empirical PKs turn out to be U-shaped for short-dated instruments and W-shaped for long-dated instruments. We find that investors are willing to pay a substantial risk premium to insure themselves against short-term price movements. The risk premium is smaller for longer-dated instruments and their traders are risk averse. The shape of the empirical PKs reveals the existence of a time-varying risk premium. The similarity between the shape of empirical PKs for Bitcoin and other markets that represent aggregate wealth shows that Bitcoin is becoming an established asset class.
We analyse robust dynamic delta hedging of bitcoin options using a set of smile-implied and other smile-adjusted deltas that are either model-free, in the sense that they are the same for every scale-invariant stochastic and/or local volatility model, or they are based on simple regime-dependent parameterisations of local volatility. These deltas are popular with option market makers in traditional assets because they are very easy to implement. Previous empirical research on dynamic delta hedging is based solely on equity index options, but analysis of our unique data on hourly historical bitcoin option prices reveals that bitcoin implied volatility curves behave very differently from those of equity index options. For call and put options with a wide range of moneyness and with synthetic constant maturities of 10, 20 and 30 days, we compare the dynamic hedging performance of different smile-adjusted deltas over two one-year periods. We also examine the use of the perpetual contract rather than the standard futures as hedging instrument because the basis risk for the perpetual is very much smaller than it is for calendar futures. Results are presented as testable statistics of hedging error variance ratios. In certain periods the use of smile-implied hedge ratios can significantly out-perform the simple BlackâScholes delta hedge, especially when using the perpetual swap as hedging instrument, where efficiency gains can exceed 30% for out-of-the-money puts, and reach an average of 15% when hedging short-term out-of-the money calls during periods when the implied volatility curve slopes upwards. The advantage of using the perpetual contract is especially evident during 2021, for the longer-term contracts for which the basis is still rather large.
Abstract Several procedures to forecast daily risk measures in cryptocurrency markets have been recently implemented in the literature. Among them, longâmemory processes, procedures taking into account the presence of extreme observations, procedures that include more than a single regime, and quantile regressionâbased models have performed substantially better than standard methods in terms of forecasting risk measures. Those procedures are revisited in this paper, and their value at risk and expected shortfall forecasting performance are evaluated using recent Bitcoin and Ethereum data that include periods of turbulence due to the COVIDâ19 pandemic, the third halving of Bitcoin, and the Lexia class action. Additionally, in order to mitigate the influence of model misspecification and enhance the forecasting performance obtained by individual models, we evaluate the use of several forecast combining strategies. Our results, based on a comprehensive backtesting exercise, reveal that, for Bitcoin, there is no single procedure outperforming all other models, but for Ethereum, there is evidence showing that the GAS model is a suitable alternative for forecasting both risk measures. We found that the combining methods were not able to outperform the better of the individual models.
Abstract We develop a continuousâtime control approach to optimal trading in a ProofâofâStake (PoS) blockchain, formulated as a consumptionâinvestment problem that aims to strike the optimal balance between a participant's (or agent's) utility from holding/trading stakes and utility from consumption. We present solutions via dynamic programming and the HamiltonâJacobiâBellman (HJB) equations. When the utility functions are linear or convex, we derive closeâform solutions and show that the bangâbang strategy is optimal (i.e., always buy or sell at full capacity). Furthermore, we bring out the explicit connection between the rate of return in trading/holding stakes and the participant's riskâadjusted valuation of the stakes. In particular, we show when a participant is riskâneutral or riskâseeking, corresponding to the riskâadjusted valuation being a martingale or a subâmartingale, the optimal strategy must be to either buy all the time, sell all the time, or first buy then sell, and with both buying and selling executed at full capacity. We also propose a riskâcontrol version of the consumptionâinvestment problem; and for a special case, the âstakeâparityâ problem, we show a meanâreverting strategy is optimal.
Decentralized Finance (DeFi) aims to use advancements in both computation and cryptography to tackle standard economic problems. It must, therefore, operate within the intersection of constraints required by both the computer science and economic domains. We explore a foundational question at the junction of those fields: is it possible to synthesize variable market-clearing risk-free yield for native tokens via smart contracts? We show using a stylized model representing a large class of existing decentralized consensus algorithms that this is not possible. This places strong bounds on what decentralized financial products can be built and constrains the shape of future developments in DeFi. Among other limitations, our results reveal that markets in DeFi are incomplete.
Since the creation of Bitcoin in 2009, digital exchanges have demonstrated that global, 24/7 and disintermediated trading is possible. By trading digital currencies, they have grown to a size impossible to ignore. To allow digital exchanges to enter the multitrillion market of securities trading and business, technology and regulators need to work hand in hand. Together, they are in a position to solve the challenges of a steep learning curve and build an efficient, convenient and, most importantly, trustable environment that can protect investors. Regulators face the challenge of channelling the path but are potentially also among the biggest beneficiaries of the inevitable transition from traditional stock exchanges to digital asset exchanges, since compliance may be ensured by design. While ensuring personal data protection and jurisdiction particularities, global standardisation and distributed ledger technology (DLT) can effectively forestall trading errors and market abuse instead of leaving them to be discovered. To generate the necessary trust for market participants to adopt, digital exchanges will have to be regulated, licensed and supervised in the same way that traditional stock exchanges are today, while safeguarding and leveraging the technological benefits that DLT carry.
In this paper, we conduct a fast calibration in the jump-diffusion model to capture the Bitcoin price dynamics, as well as the behavior of some components affecting the price itself, such as the risk of pitfalls and its ambiguous effect on the evolution of Bitcoinâs price. In addition, in our study of the Bitcoin option pricing, we find that the inclusion of jumps in returns and volatilities are significant in the historical time series of Bitcoin prices. The benefits of incorporating these jumps flow over into option pricing, as well as adequately capture the volatility smile in option prices. To the best of our knowledge, this is the first work to analyze the phenomenon of price jump risk and to interpret Bitcoin option valuation as âexceptionally ambiguousâ. Crucially, using hedging options for the Bitcoin market, we also prove some important properties: Bitcoin options follow a convex, but not strictly convex function. This property provides adequate risk assessment for convex risk measure.