Advances in Risk Management

168 THE MODELING OF WEATHER DERIVATIVE PORTFOLIO RISK

marketvalue of a portfolio of weather derivatives, one has to consider mod-
elling the fluctuations in market prices. If one assumes that market prices
are given by expectations, this is identical to the first case. If, however, one
assumes that the market contains additional supply and demand dynamics
that are also important, then this is a rather more difficult question. The
starting point for any attack on this problem would have to be an attempt
to model fluctuations in observed market prices.

8.13 CONCLUSION

We have discussed methods that can be used for the estimation of risk in
portfolios of weather derivatives. The simplest, but very limited, method is
burn analysis. To improve on burn analysis one can use simulations, and
the simplest way to do that is to use the multivariate normal distribution
for the weather indices underlying the contracts in a portfolio. However,
this method has a number of shortcomings. We discuss how some of these
shortcomings can be addressed. Some of the methods we describe are stan-
dard in industry. Most, however, are the subject of current research, and are
yet to be applied in practice. Furthermore we have highlighted a number of
areas where further research would be useful. In particular it would be ben-
eficial to develop a better understanding of methods for accurate estimation
of correlation matrices, and to explore whether there may be benefits to be
had from using copulas other than the Gaussian copula.

NOTES

1. More details can be found in books on weather derivatives such as Element Re (2002),
   Dischel (2002) or Jewson, Brix and Ziehmann (2005).


2. The earliest references we have seen for this method are Goldman Sachs (1999) and
   Zeng and Perry (2002).


3. In fact there is a shortcut for this step: see Wang (1998).


4. Thanks to Seth Padowitz for the terminology, and discussions on this issue.

REFERENCES

Alaton, P., Djehiche, B. and Stillberger, D. (2002) “On Modelling and Pricing Weather
Derivatives”,Applied Mathematical Finance, 9(1): 1–20.
Brody, D., Syroka, J. and Zervos, M. (2002) “Dynamical Pricing of Weather Derivatives”,
Quantitative Finance, 2(3): 189–98.
Caballero, R., Jewson, S. and Brix, A. (2002) “Long Memory in Surface Air Tempera-
ture: Detection, Modelling and Application to Weather Derivative Valuation”,Climate
Research, 21(4): 127–40.