Why Threshold Rehedging Does Not Replicate a Put Reliably
Summary
The document considers whether a holder of bitcoin can mimic put-option protection by shorting CME bitcoin futures above a chosen price and returning to a neutral position when the price crosses that threshold. The motivation is concern that a rising market could trigger margin calls and force the futures hedge closed. The proposed rule is a simple, discrete threshold strategy rather than a continuous option hedge.
The response explains that repeated crossings can create losses: the trader may cover above the threshold and reopen the short below it, repeatedly paying the gap between those prices. Narrower bands reduce the size of each loss but can increase how often trades occur. It compares the approach with delta hedging a short options position, noting that option market makers can spread hedging costs across a portfolio. The answer warns that the rule may be inaccurate and inefficient, but provides no quantitative comparison, transaction-cost model, or margin analysis. It also connects similar algorithmic hedging rules with portfolio insurance and cites concern about their role in the 1987 crash.
Key ideas
- A threshold futures rule can approximate downside protection, but it does not reproduce a put exactly.
- Repeated price crossings can cause the trader to cover high and reopen lower, accumulating losses.
- Tighter thresholds can mean more frequent hedging trades even if each gap is smaller.
- Option market makers can spread hedge costs across a portfolio of positions.
- The discussion offers no numerical test of the rule's performance or margin resilience.
Tags
Full text
# Can I replicate put option by trading futures? # Can I replicate put option by trading futures? Very basic question. Imagine I have some BTC (which is a bubble but I can't get rid of), and some money on an account which allows me to hedge with CME BTC futures. The problem is that if bitcoin shoots for the stars, my short position at CME will be closed by margin calls and I'll lose my hedge. The simplest strategy I have in mind, is to short after certain price (say, 8000) and switch to neutral position on CME if p > 8000 + commission. Is this feasible or do I miss something here? ## Answer by Brian B (score 4, accepted) https://quant.stackexchange.com/a/38216 This is feasible but you should be aware it is also potentially inaccurate and inefficient. What can happen to you is that $P$ will go above \$8,000, then back below, then back above, many times. Each time it goes above, you close your short at some price $\$8,000 + X$. When you reopen, you will open a new short at $\$8,000 - Y$, so you will have losses $X+Y$ and they get expensive very fast. If you reduce your "bands" for $X$ and $Y$, then you find yourself taking smaller losses, but doing so more frequently. Note that your scheme bears strong similarities to the process of hedging a short options position. For market makers in the futures options markets, it is possible to sell an option and keep $X$ and $Y$ quite small, realizing a profit (this hedging or replication is a key idea behind Black-Scholes). But that relies on maintaining an entire portfolio of options positions, in order to spread out those hedging costs on lots of contracts. Incidentally, what you describe was once called program trading and is related to portfolio insurance, which many people think was partially to blame for the 1987 crash: > Portfolio insurance, employing computer algorithms, was designed to limit an investor’s loss from a plunging market, while preserving upside gains in rising markets. It consisted primarily of derivative bets, and often involved using “stock-index futures in a rising market and selling them in a falling market,”
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