# What is the role of stochastic calculus in day-to-day trading?

I work with practical, day-to-day trading: just making money. One of my small clients recently hired a smart, new MFE. We discussed potential trading strategies for a long time. Finally, he expressed surprise that I never mentioned (much less used) stochastic calculus, which he spent many long hours studying in his MFE program. I use the products of stochastic calculus (e.g., the Black-Scholes equation) but not the calculus itself.

Now I am wondering, does stochastic calculus play a role in day-to-day trading strategies? Am I under-utilizing a potentially valuable tool?

If this client was a Wall Street investment bank that was making markets in complicated derivatives, I'm sure their research department would use stochastic calculus for modeling. But they're not, so I'm not sure how we would use stochastic calculus.

(Full disclosure: I have Masters degrees but not a PhD. I'm an applied mathematician, not a theoretician.)

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## 1 Answer

This is pure speculation:

MFE's are really tailored toward valuation models (how can we develop a model to price x swap, etc.). You don't entirely have to worry about those details in order to trade them: you're just quoted a price based on these models. But if you go in-house at a bank and are working as a product quant (structured products, etc.), then you really need to worry about these things.

Alternatively, it could be relevant to a trading strategy if you think that the current model is mispricing things and there's an arbitrage opportunity. This is why banks have put so much effort into having good models, and jump at opportunities for very minor improvements. This kind of behavior is documented in Derman's "My Life as a Quant".

Short of that, if you are simply trading an asset in order to gain a specific kind of exposure, stochastic calculus is not really used very much.

As a final note, I would point to the draft of Steven Shreve's "Stochastic Calculus and Finance" as a free reference, if you're looking for one.

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Great answer, Shane. It reminds me of Wall St quants talking about "model arb": my model prices better than your model, so I can make a profit by trading with you opportunistically. But, again, that's for the Big Boys on the Street. Your answer nicely highlights that. Thanks for the references, too. – pteetor Feb 3 '11 at 19:04