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1 Problem Setup Volly, the volatility trader runs proprietary trading algorithms in various crypto-currency markets. Volly's favorite market is the BTC/USDT pair, which has very high volume offering good liquidity and generally high volatility. We model the daily performance of Volly's algorithms as an output 0 {-1, +1}. A simple stochastic model for the performance of Volly's algorithms is a Bernoulli random variable with two separate regimes: low volatility days and high volatility days. We can treat the daily returns as a suitable proxy for intraday volatility leading to the following model: +1, w.p O IR Sa= OL 1-1, w.p 1- (1) +1, W.P 0||R. >= 1-1, w.p 1 - 0 (2) Here R, is the daily arithmetic returns at time t as P-P-1 R = (3) P-1 Volly's algorithms generally perform well on on days with large price swings and and perform worse on days of smaller price swings, so we expect 0, = 1-1, w.p 1 - 0 (2) Here R, is the daily arithmetic returns at time t as P-P-1 R = (3) P-1 Volly's algorithms generally perform well on on days with large price swings and and perform worse on days of smaller price swings, so we expect 0,