Room for a View

R. Korn and P. Wilmott

Abstract

There is no room in the classical Black-Scholes framework for the market view of an investor. The investor in derivatives needs to know the volatility of the underlying, that is the 'choppiness' of the market, but the direction is irrelevant. Suppose we have two stocks A and B having the same volatility, 20%, say. They both have a value 100 today and there are call options on these two stocks with strike of 100 and an expiry of six months. In the market these options will have the same value. If you were to invest in one of these call options, which would you choose to buy? If you are a pure speculator, we hope you will ask us 'In which direction are the two stocks expected to move in the next six months?' So, now we tell you that stock A has an expected return of 20% and stock B has an expected return of -20%. Are you indifferent between these two calls? Obviously not. Yet the pure delta hedger is. How can we reconcile these two positions?

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