In this paper, we investigate conditions to represent derivative price under XVA explicitly. As long as we consider different borrowing/lending rates, XVA problem becomes a non-linear equa- tion and this makes finding explicit solution of XVA difficult. It is shown that the associated valuation problem is actually linear under some proper conditions so that we can have the same complexity in pricing as classical pricing theory. Moreover, the conditions mentioned above is mild in the sense that it can be obtained by choosing adequate covenants between the investor and counterparty .
In this paper, we investigate conditions to convert nonlinear equations of XVA to linear equations. As we consider different borrowing/lending rates, pricing derivatives encounters a non-linear equation and this makes finding an analytic solution for the price with the XVA difficult. Thus, in general, we have to resort to expensive numerical computation. In most previous works, the attempts to find an analytic solution were conducted on a restrictive assumption that the borrowing/lending rates are same. We find conditions to relax the assumption. Moreover, the conditions are mild in the sense that it is often satisfied in practice .
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represent derivative price under XVA explicitly. As long as
convert nonlinear equations of XVA to linear equations. As
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XVA problem becomes
pricing derivatives encounters
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equa- tion
equation
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explicit solution of
an analytic solution for the price with the
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It is shown that the associated valuation problem is actually linear under some proper conditions so that we can have the same complexity in pricing as classical pricing theory.
Thus, in general, we have to resort to expensive numerical computation. In most previous works, the attempts to find an analytic solution were conducted on a restrictive assumption that the borrowing/lending rates are same. We find conditions to relax the assumption.
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mentioned above is
are
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can be obtained by choosing adequate covenants between the investor and counterparty
is often satisfied in practice