American option and default perception: The end of the risk-neutral measure

After the credit crunch and the euro crisis, the financial industry became very concerned by the credit risk. These dual market stresses pushed market participants to realize that some usual assumptions are no longer valid.  Indeed as explained in recent studies of credit, debit, and funding value adjustment, the completeness of the market does not hold anymore.  Credit and liquidity risks have pushed the industry to consider adjustment to the risk neutral premium.

Over the last decade autocallable structure have been very popular (from 2003 to 2010 the size of Autocallable Structured Products rose exponentially). In the context of very low interest rates and hudge market volatility, it becomes very interesting to invest in the autocallable structure. The coupon can be more less complex but usually a part of them are fixed and higher than the risk free rate. The call event also referred to as the trigger event is a function of the underlying performance. The autocallable is a classical option which does not represent a big challenge in terms of pricing. Given a dynamic for the underlying stock, we can price the option via a Monte Carlo simulation. The discontinuity payout (rebate or not rebate) induces two main issues

• The high Monte Carlo error which will affect our pricing and the "Greeks," price, sensitivities, produced by the finite difference.

• The dynamic hedging associate to this option is tricky because of the "Greek" instablities close to the trigger event (event which induces the call of the option). This risk which is a remaining digital risk need to be price as a hedging cost.

The American option in a default world implies a subjective decision depending on the perception of default. If our counterparty default perception is very alarming, we will be more tempted to call for the early exercise of the option.

This work draws upon an earlier article by the same author, Autocallable More American Than European?, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1924499.  That article examined the autocallable, a structured product which involves payment of more or less exotic coupons until a callable event. The digital risk at each coupon payment date induces hedge difficulties. Indeed, closer to the trigger event, the trader faces hedging difficulties at each fixing between the potential rebate and the future value of the option (which may be very different).