We introduce several regime-dependent smile-adjusted deltas and compare their efficiency with the smile-adjusted deltas that are popular with option traders. Using years of daily option prices, out-of-sample hedging performance tests for options of all moneyness and maturities and daily, weekly, or fortnightly rebalancing show that even the simplest regime-dependent smile-adjustment consistently outperforms implied BSM delta hedging and local volatility and minimum variance smile-adjustments. Markov-switching deltas offer the best performance, with delta-hedging errors often half the size of implied BSM hedging errors. During volatile markets risk reduction from regime-dependent delta hedging is much greater than during tranquil periods

No abstract

Biases in standard variance swap rates can induce substantial deviations below market rates. Defining realised variance as the sum of squared price (not log-price) changes yields an 'arithmetic' variance swap with no such biases. Its fair value has advantages over the standard variance swap rate: no discrete-monitoring or jump biases; and the same value applies for any monitoring frequency, even irregular monitoring and to any underlying, including those taking zero or negative values. We derive the fair-value for the arithmetic variance swap and compare with the standard variance swap rate by: analysing errors introduced by interpolation and integration techniques; numerical experiments for approximation accuracy; and using 23 years of FTSE 100 options data to explore the empirical properties of arithmetic variance (and higher-moment) swaps. The FTSE 100 variance risk has a strong negative correlation with the implied third moment, which can be captured using a higher-moment arithmetic swap.

No abstract

No abstract