omparing the results of
( Delta hedging with
jumps) and ( Backward
equation with jumps) we conclude that the risk neutral pricing (see
( Risk_neutral_pricing)) applies with the
following risk-neutral
SDEs:
To summarize, under the change to the risk neutral measure, drift changes to
 ,
volatility and the size of the jump do not change, intensity of the jump
changes to some function implied by the market. Hence, the historical data
(real world probability) on intensity of the jumps disapears completely from
the pricing equations.
On somewhat agressive note the above result means that some part of S&P,
Moody's and Fitch services may be replaced by a fairly simple piece of
software that would imply the credit ratings from the market.
|
