Global Risk Institute in Financial Services

Cryptocurrencies provide a unique opportunity to identify how derivatives impact spot markets. They are fully fungible and trade across multiple spot exchanges at different prices, and futures contracts were selectively introduced on Bitcoin (BTC) exchange rates against the U.S. dollar (USD) in December 2017. Following the futures introduction, we find a significantly greater increase in cross-exchange price synchronicity for BTC–USD relative to other exchange rate pairs as demonstrated by an increase in price correlations and a reduction in arbitrage opportunities and volatility. We also find support for an increase in price efficiency, market quality, and liquidity. The evidence suggests that futures contracts allowed investors to circumvent arbitrage frictions associated with short-sale constraints, arbitrage risk associated with block confirmation time, and market segmentation. Overall, our analysis supports the view that the introduction of BTC–USD futures was beneficial to the Bitcoin spot market by making the underlying prices more informative. This paper was accepted by Will Cong, Special Section of Management Science: Blockchains and Crypto Economics. Funding: The authors acknowledge financial support from the Global Risk Institute. P. Augustin acknowledges financial support from the Canadian Derivatives Institute and from the Canada Research Chair Program of the Social Sciences and Humanities Research Council Canada. The paper has benefited significantly from a fellow visit of P. Augustin at the Center for Advanced Studies Foundations of Law and Finance funded by the German Research Foundation, project FOR 2774, and from a visiting position of P. Augustin at the finance department of the University of Luxembourg facilitated through the Inter Mobility Programme of the Luxembourg National Research Fund. Supplemental Material: The online appendix and data are available at https://doi.org/10.1287/mnsc.2023.4900 .

In this paper, we analyse, modify, and apply one of the most widely used measures of systemic risk, SRISK, developed by Brownlees and Engle (in Rev Financ Stud 30:48–79, 2016). The measure is defined as the expected capital shortfall of a firm conditional on a prolonged market decline. We argue that segregated funds, also known as separate accounts in the US, should be excluded from actuarial liabilities when SRISK is calculated for insurance companies. We also demonstrate the importance of careful analysis of accounting standards when specifying the prudential capital ratio used in SRISK methodology. Based on the proposed adjustments to SRISK, we assess the systemic risk of the Canadian banking and insurance industries. It is shown that in its current implementation, the SRISK methodology substantially overestimates the systemic risk of Canadian insurance companies.

AD technology enables the computation of Jacobian-matrix (and Hessian-matrix) products directly, without first requiring the determination of the Jacobian (Hessian) matrix itself. For example, if the product JV is required where J is the m-by-n Jacobian of the differentiable mapping F : ℛn → ℛm and V is an n-by-tV matrix, then this product can be determined directly by the forward mode of AD. Specifically, (1.2) becomes

The companion AD software package, ADMAT, allows the user to compute first and second derivatives in the MATLAB environment. Chapter 4 (and parts of 7) illustrate how to efficiently apply ADMAT for structured problems. This is quite important since many practical problems are structured, and very significant efficiency gains—in space and time—are obtained by taking advantage of structure. Indeed, the structured use of ADMAT, efficiently balancing the use of forward and reverse modes of AD, can turn otherwise intractable problems of differentiation into efficient procedures. The efficiency gains are due, in part, to discovering and exploiting hidden sparsity in an apparently dense computing problem.

The basic idea behind automatic differentiation is simple: it is the chain rule.

Nonlinear minimization and solving nonlinear systems of equations often involve the computation of the Newton step. For a nonlinear system, i.e., find x ∊ ℛn such that F(x) = 0, where F : ℛn → ℛn and continuously differentiable, the determination of the Newton step typically involves two major steps: