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Last week concluded on a bearish note, as BTC closed at $26,900, marking a roughly $800 from the week's opening price. Similarly, the S&P closed at $4,350, facing resistance at the $4,400 price level. This week, the market opened with considerable volatility in Bitcoin due to a reaction to false reports about ETF approval. BTC's price surged from $27,900 to $30,000 but quickly retraced to $28,000. In line with Bitcoin's movements, Ethereum opened the day with a similar pattern and is currently hovering around the $1,600 price level.
The morning's response in the options market was swift and pronounced. The front end of the BTC volatility curve surged to over 40 vol, while mid to further-dated expiries actually experienced a 1 - 2 point decrease. Skews also reacted swiftly, with volatilities significantly favoring calls before quickly returning to previous levels upon price retracement, approximately around 0.5.
In contrast, Ethereum's volatilities did not exhibit much movement in response to the price fluctuations, and the term structure closely resembles that of the previous week. The front end of Ethereum's volatility curve stands at 35, then declines to 30 for the Nov24 expiry, gradually rising to 46 vol for the September 2024 expiry.
Last week we introduced the concept of Gamma; this week we continue the discussion and touch on general properties of gamma and trading implications. Recall that Gamma is the second derivative of option price with respect to spot, or equivalently the derivative (sensitivity) of the delta with respect to spot price. Gamma is particularly important because it reveals the convexity of options. In the context of vanilla options, positive gamma signifies that delta (the rate of change of option price with respect to spot price) is not constant. Instead, delta behaves in a convex manner relative to spot price movements. For instance, owning a call option implies that gains accelerate as the spot price rises and losses decelerate as the spot price falls. Mathematically, given a portfolio delta = Δ, the PnL impact from a change in spot price = dS, is approximately Δ*dS + ½Γ*(dS)^2, where the gamma term serves as a correction to the regular delta PnL impact of a linear position (Δ*dS).
This has interesting implications for trading, and specifically for delta hedging. Delta hedging is a strategy employed to offset or hedge an option's delta exposure by maintaining a combination of the option and a spot position in specific quantities. For example, if the options delta was 0.4, one should hold 0.4 BTC short against it. However, due to the presence of gamma, the option's delta is not constant but changes as the spot price fluctuates. Consequently, the trader needs to continually adjust the spot position to ensure that it matches the current delta of the option. According to the Black-Scholes model, this process of continuous rebalancing to delta hedge should result in positive Profit and Loss (PnL) that is directly proportional to the option's gamma. This is because of the convex nature of the option's PnL. When the spot price moves, the option's PnL tends to outperform the spot position's PnL due to the accelerating and decelerating effects explained earlier.
It is also important to note that Black Scholes is just an approximation since it is based on numerous assumptions which are not true (for example no fees or bid - ask spreads, and the ability to rebalance infinitely often). Delta hedging in practice can be much more complex and may not always yield profits. Thus some market makers will elect to delta-gamma hedge their book in order to further safeguard the value of their portfolios against movements in the underlying asset's price. To delta hedge an option with delta = Δ, one must always hold -Δ shares of the asset. Delta-gamma hedging involves using additional option positions to offset the effects of gamma, as the spot position alone does not introduce new gamma exposure. The portfolio can be mathematically expressed as P = O1 + b*S + c*O2, where O1 is the original option to hedge, S is spot price, b is the quantity of spot to hold, O2 is the additional option used for the hedge, and c is the quantity of the new option. It can be shown that b = -Γ1 / Γ2, and c = -b*Δ2 - Δ1, where Δ1, Γ1, Δ2, Γ2 are the deltas and gammas of the options used. Delta-gamma hedging is less sensitive to spot price fluctuations and necessitates less frequent rebalancing compared to a straightforward delta hedge. However, it introduces added complexity due to the need to manage multiple option positions and their other greeks like Vega.
This week Bitcoin’s combo spread volumes on Deribit show roughly the same mix of top 3 combination spreads taken, but slightly different concentrations. Call vertical and diagonal Spreads still come in as the top two which is to be expected given call side IV slope and term structure. ETH however shows a resurgence in put spreads, but strangles / straddles remain in the top 3 from last week. BTC Deribit block trade data shows that the biggest volumes were in call diagonal spreads, call spreads, and put spreads (25.7%, 19.4%, and 18.5%). Ethereum shows the highest volumes in put spreads, call ratio spreads, and strangles / straddles (24%, 21.2%, 12.5%).
BTC Combo Spread Volumes:
ETH Combo Spread Volumes:
***Data and insights as of October 16th, 2023 12:00:00 UTC
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