Chapter 2: FAQs 197
at a times series of the value of that quantity. But how
can you estimate its market price of risk? Market price
of risk is only observable through option prices. This is
the point at which practice and elegant theory start to
part company. Market price of risk sounds like a way of
calmly assessing required extra value to allow for risk.
Unfortunately there is nothing calm about the way that
markets react to risk. For example, it is quite simple to
relate the slope of the yield curve to the market price
of interest rate risk. But evidence from this suggests
that market price of risk is itself random, and should
perhaps also be modelled stochastically.
Note that when you calibrate a model to market prices
of options you are often effectively calibrating the
market price of risk. But that will typically be just a
snapshot at one point in time. If the market price of risk
is random, reflecting people’s shifting attitudes from
fear to greed and back again, then you are assuming
fixed something which is very mobile, and calibration
will not work.
There are some models in which themarketprice of
risk does not appear because they typically involve
using some form ofutility theoryapproach to find a
person’s own price for an instrument rather than the
market’s.
References and Further Reading
Ahn, H & Wilmott, P 2003b Stochastic volatility and mean-
variance analysis.Wilmottmagazine November 2003 84–90
Markowitz, H 1959Portfolio Selection: efficient diversification of
investment. John Wiley & Sons
Wilmott, P 2006Paul Wilmott On Quantitative Finance, second
edition. John Wiley & Sons
