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edult
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Joined: October 31st, 2007, 8:24 pm

counterparty exposure real world vs risk neutral interest rate model

February 25th, 2012, 3:47 am

I have seen several papers on counterparty where an exposure in the horizon is calculated by simulating factors in real world measure and then the pricing at the horizon is done risk neutrally. Does the same concept apply to interest rate models? My concern is interest rate models imply forward rates, thus at the horizon point if one wants to price zero coupon bonds through the interest rate curve the real world model implies, prices will be generated from the real world model. One solution is to simulate the zero coupon bonds with a different short rate model at the horizon; though that would be very expensive for sthg like a zero coupon bond.
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

counterparty exposure real world vs risk neutral interest rate model

February 25th, 2012, 1:06 pm

Yes. The longer answer goes along the following lines. Let's assume that you have a dynamic term structure model with N state variables. The relevance of "the risk neutral measure" is that it is one particular way to characterize the mapping from the state variables to the value of an arbitrary set of interest rate contingent claim (including bond) prices at any given point in time. Unless you are working with a pricing kernel, there is no such thing as "the interest rate curve the real world model implies". You want to use the real world measure to simulate the dynamics of your state variables, and the risk neutral measure to compute the value of contingent claims as as function of the state variables. If your model has a structure that requires that you use simulation to solve any and all valuation problems I would suggest that you may want to explore alternative models for your current purpose.
 
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edult
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counterparty exposure real world vs risk neutral interest rate model

February 26th, 2012, 10:24 pm

bearish, let me explain my concern through an example. Let's assume state variables on the interest rate curve are simulating 2 , 8, and 10year zero coupon rates. And horizon is 2 years from now. Then at the horizon you know the 2y, 8y, 10y rates, lets assume my asset is 10year to maturity zero coupon bond at the analysis date. At the horizon, this is an 8year bond. If the price of this asset is calculated by the 8year simulated zero coupon rate (state variable) at the horizon, then the price is purely driven by the real world measure.
 
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bearish
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counterparty exposure real world vs risk neutral interest rate model

February 26th, 2012, 10:41 pm

If you can directly simulate the quantity you are interested in under the P measure, you are done. You don't need to do any more work to get its price as a function of the state variables, so no need to bring in the Q measure. Compare it to simulating a portfolio of a stock and an option on the stock. If you simulate the stock price under the P measure until a given point in time before the maturity of the option, you don't need the Q measure to say anything about the stock price, but you do need it (or its equivalent) to compute the value of the option as a function of the value of the stock. If you instead were interested in the portfolio value at the maturity date of the option, then you do not need the Q measure, since you can directly compute the option value as its payoff function of the stock price on each path.