Oct

10

An interesting paper is downloadable here. The gist of the paper is that combining 30 days of historic data with implied volatility gives a better forecast of option prices than simple implied volatility. They demonstrate this by calculating the usual stats (root mean squared error of the forecast, etc.) and by running a 'trading contest'. They describe 5 rules (they call them agents) that, at the simplest, used 30 days of returns to generate a forecast of the stocks distribution, and at its most complex, used Bayes rule to combine 30 days of returns data with implied volatility data to make a forecast of the stocks distribution. They then sell (overnight) ''over priced'' options and buy ''under priced'' options. Naturally, the simple rule makes very little money and the sophisticated Bayes rule makes a ton of money

Some things I would have liked to have known that weren't mentioned:

1. They aren't buying and selling straddles, but individual options (i.e. the simulation isn't delta hedged)… and they do not differentiate between how much of their profit is do to a favorable move in the underlying, and how much of the profit/loss is due to correctly predicting the implied volatility.

2. They do not breakdown how many profitable trades were shorting options, and how many were going long options…it makes a difference to me if I make money while I'm long gamma rather than short gamma

One thing that strikes me as making this hard to try to replicate in other markets is the time structure of volatility problem  It may be okay to take 30 days of OEX/S&P futures (or spot) data and use it when deciding about options that expire quarterly, but I'm leery of trying that with options that expire monthly.  Lets say its Feb 1, and you are looking at options expiring March 1. For stock indexes, the prior January's data will not have any, err, ''structural reason'' to be terribly different from the index future performance data from Feb 1 thru March 1.  Not so with say, oil. During January, the prompt futures contract is February. The January data is using data from Jan 1 (a 30 day forward price against the February contract) through Jan 30 (a one day forward price against the February contract). If you believe (as I do) that things get more volatile as one approaches spot, the January data is a biased representation of what one expects the market to do from Feb 1 to Feb 2  (the overnight trading part of the simulation). The January historic data is a blending of variances of 30 day forwards (Jan 1's vs Jan2's observation) and overnight forward prices (Jan 30's vs. Jan31's observation), but we want to ''overnight trade'' an option on a 28 day forward contract (the March option expiring March 1) — the variances don't ''match up''.

Do any statwise people have an idea as to how I might get around this time structure of volatility problem in trying to reconstruct this simulation using oil prices? (Let's leave the seasonality problems alone for the moment).

N.B. Oil savvy specs will realize I've fudged the expiration cycle/dates a little for the sake of clarity

Dr. Alex Castaldo replies:

Academically it is an interesting paper. They were able to derive extremely messy mathematical expressions for the posterior distribution that are new to the option literature as far as I know. (Bayesian stats sounds good until you try to do the math… often you just hit a brick wall and can't get anywhere).

From a practical point of view I share Prof. Corso's concerns. There are a number of real life issues (like term structure, skew, etc) that are left out.

Also I am bothered that they use (page 17) the "mean of the implied volatilities over the 30 days preceding" and the 30 day realized volatility in their Bayesian estimator. The standard opinion in the industry is that the latest implied volatility is the best estimator and that is one of the estimators they claim they can beat.


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