In the following, we look how the results change when the continuation value is the insolvency administrator's private information and, thus, not contractible.
Consistent with the no-arbitrage valuation theory, the continuation value is the risk-neutral expectation of the discounted future cash flow, i.e.,: Fleft omega; {t}_kright)={E}^Qleft[{displaystyle sum_{j=k+1}^K exp left -{displaystyle underset{t_k}{overset_{t_j}}{int }}rleft -{displaystyleds}right)Cleft(omega, {t}_j;{t}_k,Tright)Big|{Im}_{t_k}}right].
Within this context, whenever it is possible to exercise the option, the continuation value can be expressed as a linear combination of orthogonal basis functions, such as Power, Legendre and Laguerre polynomials.
The LSM method contributes by approximating the continuation value that is the conditional expectation of time (t) (if exercise is still allowed) of future optimal payoffs from the contingent claim.
The idea of the Least-Squares Monte Carlo Method is to approximate the continuation value by using least-squares regression at every moment in which it is possible to exercise the option.
From Eq. (10), the problem boils down to how to find the continuation value in order to apply Eq. (9).
If only J < ∞ are elements of the basis that can be used to approximate Ф, the continuation value becomes: {Phi}^Jleft {t}_n,{P}_{t_n}right)={displaystyle {sum}_{j=0}^M{varphi}_j t){L}_jleft t,{P}_tright)} (12).
Moreover, the insolvency administrator's preferences represented by u and r have to be observable and a verifiable and unbiased estimator of the continuation value must be available.
It is based on the continuation of values along the given ray field.
The value in a continuation increases with (theta) but is not perfectly predictable as a result of uncertain future events.
