Chapter 3
Modelling and Rating Dynamic
Proportion Portfolio Insurance
products
Summer 2007's turmoil in global credit markets resulted in a
significant increase in volatility, thereby threatening the rating stability of
many existing structured products including CSO tranches and CPDOs. A
straightforward response to such a volatile environment is to cap the downside
Mark-to-Market risk by adding a capital protection feature to new structured
products: Constant Porportion Portfolio Insurance (CPPI) products and their
most recent offshoots, Dynamic Proportion Indurance Products (DPPI), belong to
that category.
We shall first recall the main principles of Moody's approach
for measuring risks in order to rate CPDO and CPPI/DPPI products and outline
its main assumptions in modelling risk factors. We shall then describe the
DPPI's major risk sensitivities and present some of its key structuring
features in order to mitigate those risks. Finally, we shall analyze the DPPI's
behaviour under several stress-scenarios.
3.1 Moody's approach to rating CPDO and CPPI/DPPI
products
3.1.1 Historical vs risk-neutral probability measures
Before going into the details of rating and pricing DPPI
products, we shall address the following question: why do investment banks
price their structured products under a risk neutral probability measure while
rating agencies rate them under the historical probability measure?
Rating agencies evaluate loss ditributions under the
historical probability measure because investors are mainly concerned with
knowing how likely it is that they are going to lose money in our real
«historical» world. They don't care about such a likelihood in a
risk-neutral world. Doing so requires rating agencies to estimate future
historical default probabilities and loss distributions, the parametres of
which are calibrated statistically, whenever it is possible, on past historical
data.
On the other hand, investment banks are concerned with pricing
such products by evaluating the associated hedging costs. Fundamental results
such as HarrissonPliska's no-arbitrage pricing theorem and Black-Scholes
conclusions ensure that:
· in a viable and complete market, there exists only one
probability measure Q called «risk-neutral» under which discounted
asset prices are martingales;
· there exists a self-financing portfolio that replicates
the product's payoff.
Girsanov's theorem allows us to relate historical and risk
neutral probability measures through the notion of risk premium, which in turn
can be interpreted in terms of risk aversion: under most market circumstances,
real-world investors are naturally risk-averse and hence require to be paid an
extra return for bearing default risk as compared to its true historical
insurance cost. Hence coexisting historical and risk-neutral probability
measures serve different purposes: the historical approach prevails for
weighting future real-world scenarios and building risk measures such as the
Value-at-Risk, while the risk-neutral framework allows the pricing and the
hedging of traded securities.
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