I am writing a master thesis and I am stuck on a question, therefore I would be more than thankful if any of you could help me.
I am modeling Wrong Way Risk. I use an over the counter forward contract between two counterparties. Let's say that I want to know how much I can lose due to my counterpart defaulting. The basic formula would be:
Probable Loss=Prob. of default*Expected Value of the contract*(1-Recovery rate)
To compute the value of the contract I use risk neutral valuation method. My issue is that I want to calibrate the probability of default from real default events, thus I will have a real world probability of default (not the one implied by the market spreads). I am allowed to do so? If no, what would be the alternative, valuing the forward contract under real world expectations?
So I should understand that if I want to compute an expected loss from a derivative contract, due to counterpart default risk, I can use the real default probabilities. On the other hand, when I want to price the contract and include the risk adjustment due to the same risk of default of my counterpart than I should use the default probabilities implied by the market, as those represent a general consensus as how everyone believes how risky the company is, and thus how much they would pay for the same contract?
There is more to it than probable loss as you have given. You need to take into consideration the implied volatilities of counterparty risk as well as the dependencies (hint: copulas). Default risk of a counterparty is very much dependent on just on the PD but how it risk correlation to the firm that's related to the industry.
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