Sophisticated vulgarity 1

By Emanuel Derman
July 28, 2011

I said I would try to explain what I mean by sophisticated vulgarity in financial modeling, which I will do by imperfect analogy.

Suppose you are thinking of manufacturing tropical fruit salad and you are going to market it in the USA. And suppose there is no tropical fruit salad currently being sold.

Your fruit salad will contain mangos, papayas, passion fruit, coconuts, litchis, kumquats and loquats. Once you quote a price to Whole Foods, your distributor, you will be committed to it, and you need to give them a price. So, you want to figure out how much to plan on charging e for a can of tropical fruit salad which you haven’t actually produced yet. There are a variety of ways you could do it.

1. You could model out how much it would cost to import the raw ingredients –  mangos, papayas, lychees, syrup  and loquats, etc. –from cost at their source, taking account of shipping, shrinkage, insurance, canning, etc, and determine a fair price, allowing for profit. That’s a direct way to proceed, subject to uncertainty about what these costs will be in the future. In that sense it’s a little akin to Black-Scholes modeling of options, which makes assumption about the future that may not/ will not turn out to be true, and then figures out the cost of synthesizing an option.

2. You could build a deeper model, and instead of accepting the market price for the raw mangos, passion fruit, papayas, lychees and loquats  and sugar yourself as a proxy for future fruit prices, you could try to estimate it ab initio, taking into account of the cost of seeds, fertilizer, farmland, your inexperience in raising strange crops, labor etc, and determine the cost that way. That’s deep, but it needs a lot of knowledge you don’t have and will therefore necessarily misestimate. This is a little akin to stochastic volatility models, where you make assumptions about things you really have not much experimental information on. Ambitious, but …

3. Finally, you could be sophisticated. Though this example is a little contrived, I hope it gets at the idea. You can think of tropical fruit salad as a sort of mixture of other processed products already available in the market  that come closer than the raw ingredients to what you are trying to make. Thus, think of the fruit salad as involving Tropical Fruit Life Savers (very tasty!), for example, plus commercial passion fruit juice sweetened with apple juice,  Puerto Rican canned guava desserts filled with cottage cheese, and so on. Then model your tropical fruit salad as a mixture of all of these (and other) processed foods, long some of them, short apple juice and cottage cheese. The price of your tropical fruit salad is then related to the price of processed foods that come close to it.

This is similar to the so-called Vanna Volga heuristic method (I don’t want to call it a theory or even a model)  in options pricing. It’s sophisticated because you have to think about how to make your salad out of other already processed complicated things. It’s vulgar in that you use only things that the crowds can already buy.

I like it, and even a lot of people who are capable of method 2 in theory often use method 3 in practice, pragmatically. I like it because it uses the market values of one set of processed foods to find the market value of another, rather than starting from raw foods. Using processed foods as input removes a lot of the modeling uncertainties.

 

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Next question for this method (sophisticated vulgarity) is to estimate its constraints. if price for Puerto Rican canned guava desserts has changed in some manner according to reasons specific for the market of this product, how should fruit salad price behave? if fruit salad price is determined by chosen set of ingridients someone can construct fruit salad from another ingridients and gain “risk-free profit”. to avoid this our initial set of ingridients should be unique for our fruit salad, in other words there should be no another set of ingridients that can be used to construct same fruit salad. even in this case first question remains the same: what fruit salad price should do when price of one of ingridients changes? if fruit salad price changes in the same direction and with same amplitude (generally speaking, according to some predefined strict law) then it means that we can use fruit salad for getting its ingridients as separate valuable assets (if guava desserts became expensive and fruit salad is cheap, then buy fruit salad, decompose it, sell guava and take profit). So the idea is that for this method we should clarify “relationship” between ingridient and final product. If it is done then such pricing is relevant.

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