You use the yield curve slope and calibrate to implied vols. Nowhere should you calibrate to historical data. Consult the book by Martingale Methods in Financial Modelling for more details.

Try Karatzas and Shreve, exercise 3.36, page 167. You could expand the X in Hermite polynomials and then express the Hermite polynomial of M as a multiple stochastic integral using the aforementioned exercise.(caveat: I have never done this before, but this method sounds reasonable)

What about using the superhedging price? Are there upper bounds on this or something?

<t>If the OU process models an interest rate process, then you *assume* that you are already in the risk-neutral measure and then calibrate the drift to bond prices to get a no-arbitrage model.If the OU process models a stock price process, then you have a problem of having negative prices with posi...

Are we talking about conditional LGDs here or unconditional LGDs?

<r>Hi Guy,I remember you from university days. How is life treating you?There are lots of swap market models about - I am pretty sure there would be a FX version of one somewhere. There is something about this in the final chapter of the Musiela/Rutkowski book on Martingale Methods in Financial Mode...

Look in Karatzas and Shreve. They get the Laplace transform of hitting times for Brownian motion - they use a combo of Girsanov and strong markov property.

This is an Asian option. I am no expert in these contracts, but the references on this page look reasonable: http://www.stat.columbia.edu/~vecer/