## 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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