I am preparing a paper about mitigating assessment failures for option pricing models. For the sake of simpliciy, suppose we are talkin about European options. In basic terms, what I would like to say is

  • Suppose you have two option pricing models (say A and B) and two contract data sets (say, X and Y). X and Y belong to the same underlying asset but different time periods $[T_0^x,T_T^x]$ and $[T_0^y,T_T^y]$. Also suppose Y is at a later date than X.
  • I price all the contracts in those data sets out-of-sample using continuously updated fitted parameters. (i.e. For contracts at time $T_\tau$ I use data from $T_{\tau^\prime}, \tau^\prime < \tau$).
  • I calculate the pricing errors for each contract in the data sets $\epsilon(\hat{P^A_i},P_i)$ (say I use ARPE = $|\hat{P_i}-P_i|/P_i$).
  • According to my performance metric, suppose model A shows better results than B for data set X but worse results for data set Y.
  • Someone checking my experiment during a time between X and Y would think A is a better model than B (given the experiment limitations). But results of X is not an indicator of future performance, hence the results of Y.
  • Now, generalize it a bit by with multiple time frames (X, Y, Z, W, Q....) and contract space is divided into groups of moneyness and maturity (e.g. contracts between 30-90 days ATM options). Also suppose better model changes frequently (i.e. for X A is better, for Y B is better but for Z A is better again for the same moneyness maturity group).
  • To sum up, my pricing errors within the groups have low predictive power. I want to "decrease the prediction error of the pricing errors".

Here is my methodology to improve

  • Instead of predefined groups, I employ some machine learning algorithms to form the groups dynamically using pricing errors of the past data. I update the groups periodically.
  • I use 10 different data sets for cross validation. For each data sets I train my ML algorithms using the past 6-months of pricing errors to predict the next week's pricing errors. My performance metric is the difference between the predicted pricing error vs the actual pricing error for each contract.
  • Then I assess the effectiveness of each ML algorithm to find the most suitable algorithm for the given pricing model.
  • Here is a previous work.

My questions are

  • If I use relative errors I sometimes get huge errors because of the denominator effect. For instance, for the same group, if I estimate the average ARPE as 0.5% but a contract has a ARPE of 5% the relative error of the prediction error is 900%! Is there a way to mitigate that? (I am thinking about using direct absolute errors.)
  • My data has strong dependence as my underlying is the same and for the same time point only time to maturity and moneyness differences.
  • What types of analyses or tests can I do to explain these shifts in both pricing errors and prediction errors? Until now, I was just doing aggregate analyses based on data sets and as a whole. (For instance, I was thinking about making the same experiment with IV errors and compare models.)
  • What should be my approach to present it to an audience with little background on quantitative finance but are proficient in statistics and data mining?

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