凸状調整とタイミング調整の由来

最近債券と利子の派生証券の値段に影響する凸状とタイミング調整にかんして学んでいます。
The convexity adjustment can be derived from either the Taylor Series about the forward rate(Hull, Bond price in terms of yt about y0, then taking expectation about both sides) or by expressing y as a Geometric Brownian Motion and using Ito's Lemma to derive the bond price formula (solve for drift, mult by 1, it seems, as we are effectively finding the yield on a bond with maturity of T+!).
The Timing Adjustment is more difficult, as it involves the use of the Numeraire Ratio to obtain the change in the expected growth rate of the yield based on the volatility of the Bond Price. The volatility of the bond price is derived from Ito's Lemma. The adjustment to the observed forward rate is exp(-alphav*t), where alphav is the expected growth rate adjustment.
The final expression (from Hull)is:
E2(v1)=E1(v1)*exp(-(p*sigmaf*sigmar*R0*T1*(T2-T1)/(1+R0/m))
This is the general form of the expectation in a forward risk neutral world with respect to P(t,T2) of a variable v considering the timing adjustment where F is the forward value of v, and p is the correlation between F and the current interest rate R. If F and R are the same, the formula simplifies to:
E2(v1)=E1(v1)*exp(-(sigmar^2*R0*T1*(T2-T1)/(1+R0/m))
One problem with this formula is that it is based on the assumption of instantaneous perfect negative correlation between the forward bond price G and the forward interest rate R, which has yet to be proven. Intuitively, this makes sense, as the more the interest rate rises above the mean, the more the bond price falls below the mean.
The timing adjustment is theoretically interesting, as, if positive, it adjusts the payoff to compensate for the added risk of being in a world that is forward risk neutral with respect to a bond P(0,t2) as opposed to one forward risk neutral wrt P(0,t1).
しかし悩むところが沢山ある。
The timing adjustment involved a numeraire change while the convexity adjustment does not. The convexity adjustment is based on the fact that, since the cash flow does not occur one period after the rate observation, the forward rate backed out from bond prices does not apply. Instead, the expected rate obtained by moving along the forward yield curve (mapping time to forward yield starting from that time) would. It is unclear whether LIBOR in arrears payments involve convexity adjustment (it seems that they do). The convexity adjustment seems to be a special case of a timing adjustment applied to interest rates where the cash flow is moved one compounding period backwards.