Principles of Quantitative Development

4.2 MODEL-CENTRIC VIEW

A model-centric view is what quants hold on to. Quants are the mathematical brains of the bank. Their deliverables are mainly pricing models. A pricing model is the end result of a set of assumptions on how the market evolves and how the evolution reflects on the value of the trade. Once the pricing model is developed and delivered, the quant can consider his task accomplished for the particular product under consideration. Therefore, their natural view of trades is from this angle.

A simple example may help elucidate the model-centric view. In order to come up with a model to price an equity option, we can make a reasonable assumption about equity prices that the daily returns of a particular stock is a random variable with a Gaussian distribution. The resulting probability distribution of the spot price of the underlying equity is the well-known lognormal distribution. The standard deviation of the daily returns is related to the volatility of the stock, which we can determine from historical price data. Once we annualize it (to consider the standard deviation of the annual returns), we get the stock volatility.

If we make a further assumption that the volatility is constant over time, we have all the ingredients for the famous Black–Scholes partial differential equation, which equates the returns of a portfolio consisting of the option and a fraction of its underlying to the risk-free rate of return. The Nobel Prize winning solution to this equation is ...