150 Frequently Asked Questions In Quantitative Finance
Whenever you have risk that you can’t get rid of you
have to ask how that risk should be valued. The more
risk the more return you expect to make in excess of
the risk-free rate. This introduces the idea of the mar-
ket price of risk. Technically in this case it introduces
the market price ofvolatilityrisk. This measures the
excess expected return in relation to unhedgeable risk.
Now all options on this stock with the random volatility
have the same sort of unhedgeable risk, some may have
more or less risk than others but they are all exposed to
volatility risk. The end result is a pricing model which
explicitly contains this market price of risk parameter.
This ensures that the prices of all options are consistent
with each other via this ‘universal’ parameter. Another
interpretation is that you price options in terms of the
prices of other options.
References and Further Reading
Joshi, M 2003The Concepts and Practice of Mathematical
Finance.CUP
Merton, RC 1976 Option pricing when underlying stock returns
are discontinuous.Journal of Financial Economics 3 125–44
Wilmott, P 2006Paul Wilmott On Quantitative Finance, second
edition. John Wiley & Sons
