If I remember my finance right you never want to use your option until the very end since baked into the price of an option there is a premium for time which decreases the closer it is to expiration. That is why black sholes works pretty well.
By using your option you probably meant buying and later exercising it. Here is a non-speculative, non-hedging buyer's statement. At an ITM strike profitable for exercising but still listed, it's better to re-sell rather than exercise because the option price is always higher that the instant payoff. This is why implied volatilities at listed ITM strikes are pumped up, causing the smile and skew. It's better to exercise sooner because with time you lose in the option premium you could reclaim. If the strike is no longer listed (this may happen if the underlying moves ITM too far from the strike and the option becomes too expensive and, as a result, even more beneficial to exercise), exercising it sooner or later is your choice. However, again, it makes a better sence to exercise it immediately and lock your profit from a risk of potential underlying moves due to the drift (alpha). Holding the option to the very end in a European way in general is not good because, as you correctly mentioned, the premium for time decreases with getting closer to the expiration and you just lose the money you initially paid for the option. An early exercise also gives you more of instant flexibility in your further trading decisions.
To explain that, you first need to understand what options are.
Options are a financial instrument where you can make bets on the market. To give you a simple example of an option, suppose you have a house worth 250k that you want to sell. You want to sell it within a year, but you are afraid that your house might lose value within that year (this is called the maturity). You might decide to instead sell an option contract for $5k, pricing the house at $250k which can be exercised within a year. What does this mean? This means that as a buyer, I pay $5k for this contract for the right to buy the underlying asset at $250k at any point within that year. The buyer is betting that the house value might appreciate beyond $250k, and the seller wants to protect themselves from the scenario that their house value depreciates. In general. options are all about betting what will happen in the future.
The problem now is in pricing your option contract. The earliest and most famous model of pricing comes from the Black Scholes model for pricing European options. With European options, you only exercise your option at the end of the maturity of the contract. However, with American options, things are a lot more complex, since the buy may decide to exercise their option at anytime within the maturity period. Moreover 99% of the industry trades with American options. For pricing American Options, the best method is to use a binomial or trinomial tree with many nodes (I will let you look up what those are).
The problem with the binomial and trinomial tree is that, it's very slow. You could lower the number of nodes in your tree, but then you lose accuracy. There are analytical solutions like Ju-Zhong which are very fast. Unfortunately such approximations tend to lose accuracy, and their error blows up. Finding an accurate approximation for pricing American options is a significant breakthrough for the industry. This problem has been eluding the best researchers in the field for decades.
What we have is an analytical solution to option pricing that is very fast, and highly accurate.
Why are we interested in option pricing? For one thing, it is a $500+ trillion dollar industry, and a lot of money is being lost in pricing errors. More importantly, if you are given an option contract, you can infer the implied volatility of the underlying asset (volatility is the degree of variation of the price of the underlying asset; could be stocks, real-estate etc.) . Since our solution is highly accurate and fast, we can extract the implied volatility in real time, along with the associated partial derivatives and make real time decision and assessments on the market.
it is a $500+ trillion dollar industry, and a lot of money is being lost in pricing errors
If I had a magical algorithm that was so much better than what was out there, I'd keep it to myself for about a year or two. If I could capture about 0.2% of the value of that industry, I'd increase my net worth to about 1 trillion dollars. Surely it couldn't be that hard to squeeze 0.2% of inefficiency out of options?
IOW, "if you're so smart, why aren't you rich?"
I never could understand why people want to share these sorts of breakthroughs with the world, rather than use them to become wealthy beyond anyone's wildest dreams.
They are not sharing it: "Oquant approximation (prop mathematical algorithm)"
They just derive more value from selling this to everyone than from investing in-house. Partly because if you want to get some alpha in hft or whatnot you probably need a lot of other things (networks, lots of capital, etc.)
Yeah, it's computation as a service - API access and custom hardware DLL to HFT firms or algo shops. There will be a cloud service - options intelligence platform, and it's going to include many new type of analytics around derivatives.
So three ways to test us is, first by comparisons you can use the options calculator (demo.oquant.com). Second, free API access so you can run it on your own datasets from CBOE or historical/live to see the differences (we'll provide live data services soon too). Lastly, we'll be uploading more numerical tests with charts and etc to show clearly we have the most accurate and fastest algorithm.
