Hi Everyone,

I have a developed a more accurate model for pricing American options - at the frequency of the 150 node tree and precision of the 10,000 nodes. Building upon this discovery, I have developed a method of pricing American style options contracts paying dividends 100% accurately from extracting the implications from the term structure also in real-time.

I have ran a hypothetical scenario on a call option which produced a 2% error when computed with the 150 node tree compared to my pricing model. I know that my model represents the true options price because as I add nodes (up to 40k) to the tree, the price converges towards mine.
How can I use this 2% error to build profitable arbitrage trading strategies for options markets. Furthermore, I would love to speak with and possibly work with anyone who has options arbitrage trading experience.

Thank you

The problem is that there is no "true options price" because discrete dividend handling is quite model dependent and the choice of model is quite contentious. By your mention of a tree, I will guess you are working under Black-Scholes assumptions, but even there there are various types of models: escrowed dividends, piecewise GBM, and other types.  And this is all before even attempting to project distant dividend amounts.  

There are some charts at the link below that show some of the possibilities for puts. For calls, you might check out 'Back to Basics ...'  by Haug, Haug, and Lewis.

   

This is a good example of precision vs accuracy.

In high freq trading speed is relevant and the markets view on future dividend won't change much during the day. A fast model will have benefits for this sector, although in practice one can eliminate computational speed bottlenecks partially by precomputing tables before the trading starts.

If you want precision then model choice factors will be more important than numerical precision. E.g. some firms I know see dividend as a stochastic factor: -did you know there are tradable dividend futures that can be used for proxy hedging dividend risk-?  There is also a coupling between stock price and expected dividends: it the stock goes to zero you can bet you won't get any future dividend no more! These details are described in the paper Alan mentioned.

The way you model interest rates is also important. If prices go up then so will the probability that you early exercise American calls, and if so the 'duration' of your option will shorten. You will need a interest rate term structure (which should be easy since you mentioned "nodes" in your method), but some people use stochastic interest rates (the volatility of interest rates is not zero). This is however not the most relevant model element at the moment.

The most important factor you need to get right is volatility. Not just switching to stochastic non-constant volatility of the underlying, but what you really trade is the dynamics of the implied volatility surface of the derivatives (which is more about expected future market vol).

..these are just a few examples of model elements that impact accuracy more than numerical precision imo.

And not forgetting Chapter 9 of Alan's recent book on Volatility.

And not forgetting Chapter 9 of Alan's recent book on Volatility.

And the front matter section You two had some great discussions.