Evaluating Call Buying with Price-Move Probabilities
Summary
The document asks how to judge whether buying calls can be profitable when a trader has estimates for the probability and size of short-term stock moves. It frames the problem in terms of expected gains and losses, noting that a high win rate alone may not ensure profitability when losses can be large. The examples vary the probability, magnitude, and timing of upward and downward moves, and ask how strike choice and the intention to sell or exercise affect outcomes.
The response offers only a starting point rather than a worked calculation. It suggests using option Greeks to assess how option prices respond to market conditions and points toward bull and bear spreads as ways to shape risk and payoff probabilities. It also flags that probability estimates based on Brownian price models rely on assumptions that may be questionable. No option-pricing method, break-even formula, strategy parameters, or evidence of profitability is supplied, so the discussion does not answer which call strategy would have positive expected value. A usable estimate would need option prices and a specified distribution of future prices.
Key ideas
- A favorable probability of an upward move does not by itself establish that long calls have positive expected value.
- Option profitability depends on both the size and likelihood of price moves and the option’s price.
- Greeks describe option-price sensitivity to market conditions and can inform scenario analysis.
- Spreads can alter the payoff and risk profile compared with buying a call outright.
- Probability estimates derived from Brownian-motion assumptions have model limitations.
Tags
Full text
# When to expect profitability of a call options buying strategy # When to expect profitability of a call options buying strategy When could we expect consistent profitability of a call options buying strategy given specific statistical assumptions about X% chance of a stock price moving up by Y% within 1-5 days (or Z number of days). And what call options buying trading strategy parameters would be recommended to utilize to achieve such expected profitability? For example an average casino would have 50.5% - 55.9% odds on Blackjack and be consistently profitable. Not sure if similar expectations can be applied to stock trading (winning average x% y% of the time vs losing average z%) because of large swings in loss percentages unless using stop-loss which then limits the number of times we may win. However, as options can be used to limit losses, I’m assuming there may be a specific way to calculate expected break even point and profitability when trading stock options based on statistically predicting specific stock price increase. Examples: - Can I expect profitably when buying call options given statistical 50% chance of stock A moving up by 6% vs 50% chance of moving down by 3% within 2 days. - Can I expect profitably when buying call options given statistical 60% chance of stock A moving up by 3% vs 40% chance of moving down by 3% within 5 days. - Can I expect profitably when buying call options given statistical 60% chance of stock A moving up by 3% vs 40% chance of moving down by 5% within 5 days. - Can I expect profitably when buying call options given statistical 75% chance of stock A moving up by 3% vs 25% chance of moving down by 10% within 5 days. As an example of specific stock we can use FB, currently priced at $140.34, with the following options chain: https://finance.yahoo.com/quote/FB/options?p=FB&date=1490918400 Furthermore, because of short-term expectations, I’d like to consider multiple options strike selection approaches: - a) In-the-money, with intent to sell purchased calls within several days - b) In-the-money, with intent to exercise them - c) Near-the-money - d) Far out-of-the-money, with intent to sell them within several days, for example expecting a \$0.10 option to raise in price above $0.20 (100%) when stock price approaches in-the-money level. NOTE: I'm looking for layman-level answers in a way similar to casinos explaining their odds. I was thinking about posting this question in http://money.stackexchange.com, but as an answer may require some math and degree of quantitative experience, I decided to post it here with hope that I can still get an answer in the form of basic math vs advanced quant formulas, especially as the answer could be helpful to anyone starting trading options. ## Answer by hasselhoff_wth (score -1) https://quant.stackexchange.com/a/80318 https://tradeoptionswithme.com/options-probabilities-explained/ super old post, but figured if someone else is looking it might help. This link might be a decent place to get you started. The greeks which are variables that measure the sensitivity of option prices to market conditions are a great way to estimate some of this probability you're asking about. Some of the assumptions of this particular article are potentially questionable, like that asset prices are brownian motion, but nonetheless, this is a good place to start. Also looking into bull and bear spreads as a way to control the probabilities and risk.
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