Pricing of options is usually done (as was done in BSM model) using the dynamic hedging strategy. Today, we have algorithmic trading so a question naturally arises. Are options priced fairly based on other possible algorithmic trading strategies?
Case in point the strangle to straddle conversion by rolling over the legs of the strangle as and when the stock price moves. I love to take the example of Nvidia as it has actually been working out for me so far. I bought a 4 month out strangle (and I will leave out the details as that will drift us away from the main point) and I kept moving the legs of the strangle as and when the stock price drifted away from the original strike by $50. I am now having a straddle for significantly lower price than the current straddle price for the same expiry and strike.
Going forward, if I keep rolling the legs, I will have a gut with increasing width of strike overlap (thereby increasing minimum payoff at the time of expiry).
Question is not about the strategy above. The question is about the option pricing using various algorithms possible using algorithmic calculus on various legs of the options (and beyond). Pricing options using a specific algorithm will result in a specific price. BSM uses dynamic hedging and prices options based on the various trajectories that the stock price can take assuming a known mean and variance (IMO an incorrect hypothesis which definitely fails to work with stock log-returns).
But using the same (incorrect) hypothesis, we can also price options based on other trading strategies like the one I pointed out. Then the question arises — what if the two prices resulting from two trading strategies result in vastly different prices? If the actual price is closer to the first pricing strategy which is lower, then we know that it is underpriced based on the second strategy.
Assuming we have a portfolio of strategies, if markets were to be efficient, the pricing should be the same no matter which strategy is used to price the options. Is this true in reality?
Also, if you can point me to references that price options without assuming much about the distribution of the returns and possibly using a different underlying strategy than dynamic hedging, I would love to know about it.
Option pricing and the underlying trading strategy
byu/Study_Queasy inoptions
Posted by Study_Queasy
2 Comments
No they are not perfectly priced and the larger the bid ask spread the more volatile. You won’t find more than a penny or two spread on high quality blue chip options. All of the strike prices on a chain do not behave the same. Some go up more than others. Each one is subject to supply and demand at any given time. Check out stop loss and stop limit orders to chase prices up and sell only if they come back down.
There are some really simple books on how to trade options. Covered calls are the best way to start. Learn the mechanics of the trades and start with some wins that hedge or lock in profit on shares you own. Sell to open. Buy to close. Buy to open. Sell to close. When you know what that means without having to think you’re in a good spot.