Convexity cost refers to the negative financial impact experienced by a portfolio due to changes in market volatility, particularly when hedging derivatives positions. This cost arises from the non-linear relationship between an option’s price and the underlying asset’s price, quantified by the second-order Greek, gamma. When a portfolio has negative convexity, or negative gamma, the delta changes in an unfavorable direction, requiring more frequent and costly rebalancing to maintain a delta-neutral position.
Implication
The cost of convexity is a critical consideration for options market makers who sell options and thus typically hold negative gamma positions. During periods of high volatility, the price movements of the underlying asset accelerate the losses on the short option position, while simultaneously increasing the cost of adjusting the hedge. This dynamic creates a significant risk exposure, particularly in high-leverage crypto derivatives markets where sudden price spikes are common.
Measurement
Quantifying convexity cost involves calculating the expected cost of dynamic hedging over a specific time horizon under various volatility assumptions. The calculation considers transaction costs and the frequency of rebalancing required to manage the portfolio’s changing delta. Effective risk management strategies seek to minimize this cost by optimizing rebalancing frequency and incorporating volatility forecasts into pricing models.
