This paper expresses the price of a spread option as the sum of the prices of two compound options. One compound option is to exchange vanilla call options on the two underlying assets and the other is to exchange the corresponding put options. This way we derive a new analytic approximation for...

There are two unique volatility surfaces associated with any arbitrage-free set of standard European option prices, the implied volatility surface and the local volatility surface. Several papers have discussed the stochastic differential equations for implied volatilities that are consistent...

Under the new capital accord stress tests are to be included in market risk regulatory capital calculations. This development necessitates a coherent and objective framework for stress testing portfolios exposed to market risk. Following recent criticism of stress testing methods our tests are...

We analyse minute-level multi-dimensional information flows within and between bitcoin spot and derivatives. We show that perpetual swaps and futures traded on the unregulated exchanges Huobi, OKEx and BitMEX are much the strongest instruments for bitcoin price discovery and we examine potential...

A later version of this paper has been published in the Journal of Financial Stability (Volume 50, October 2020, Article Number 100776).When trading volumes are high, bitcoin futures on the Chicago Mercantile Exchange (CME) and -- until recently -- the Chicago Board Options Exchange (CBOE) lead...

Market betas of bitcoin relative to a broad crypto market index vary considerably, depending on the data source and the index selected. Even greater differences are found for ether and other cryptocurrencies. An in-depth exploration of the cause of these discrepancies reveals a long-standing...