I was thinking about the actual need for creating quantitative financial models, especially for derivative products. Consider simple calls and puts for different strikes and expiries on stocks and indices - the prices of these are determined through an online auction in the exchange. We have the Black-Scholes model to predict prices as well, but in reality, the model is actually used to plot the implied vol surface. Thus, for liquid derivatives, the prices are market-driven rather than model-driven.

Of course for exotic products, the Carr-Madan formula can help us calculate the prices from the call-put prices. These model-prices can then provide the market-maker an estimate to negotiate the talks with the buyer.

So my question is, what are the overarching needs for models in the quant finance industry? In other words, how does having sophisticated quants provide an edge to the investment banks dealing with derivatives?

  • $\begingroup$ The Carr-Madan formula only applies to European-style options which depend on the terminal value only (say binary/gap/power options). But what about American-style options? What about barrier and Asian options? What about multi-asset options? $\endgroup$ – Kevin Mar 5 '20 at 16:53
  • $\begingroup$ If you have a model you will usually be able to use that model to break down the instrument into its various risk parameters, sensitivities, and associated hedging instruments. $\endgroup$ – roz Mar 5 '20 at 16:59
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    $\begingroup$ @Bravo Not necessarily. What do you do if you don't have many traded vanilla options for a particular underlying? The Carr-Madan formula then does not really help (you need options with many strikes). There are many markets and products without a direct reference market. What about small stocks, volatility or interest rates derivatives? As roz said, models ease risk management with options. Real options are important tools in investment decisions and are model based (admittely, not high level maths here). Also quants work on fast implementations tailored to certain models/products. $\endgroup$ – Kevin Mar 5 '20 at 17:11
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    $\begingroup$ Even if you are market making something super liquid and just sitting on nbbo you still need some sort of model to manage the risk. Outside of banks (which are prohibited from prop trading) you may also want to be taking a prop view as opposed to simply market making. If you are doing that then you definitely need some model to tell you theo values. $\endgroup$ – roz Mar 5 '20 at 17:24
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    $\begingroup$ Something to bear in mind is that, without a model, the PnL of a complex derivative is pretty much a black box. Ok, so this exotic option moves 50bps in value, but why? Models allow to represent the price of the option in terms of different parameters (vol, corr spot-vol, mean-reversion etc.) and thus provide a breakdown of the option’s PnL, e.g. we lost because corr between spot and its vol moved against us, but vol itself moved enough to make up for the loss and end up positive. In other words: risk management (and PnL accounting too). $\endgroup$ – Daneel Olivaw Mar 5 '20 at 19:54

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