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Hi,
I have a question about page 528 in "Paul Wilmott on Quantitative Finance, Volume 2", 31.4.2.
The working that is shown explains how to obtain a Taylor series solution to the bond pricing equation for short times to expiry. I understand the working until he says "By equating powers of (T - t) we find that a(r) = -r, b(r) = 1/2 * r^2 - 1/2 * (u - lambda * w)". I just don't see how to obtain these 2 values from the "plugged in" version of the BPE.
Could anyone elaborate on how a(r) and b(r) are extracted? I assume it's trivial, but somehow I don't see it. Thanks.
I have a question about page 528 in "Paul Wilmott on Quantitative Finance, Volume 2", 31.4.2.
The working that is shown explains how to obtain a Taylor series solution to the bond pricing equation for short times to expiry. I understand the working until he says "By equating powers of (T - t) we find that a(r) = -r, b(r) = 1/2 * r^2 - 1/2 * (u - lambda * w)". I just don't see how to obtain these 2 values from the "plugged in" version of the BPE.
Could anyone elaborate on how a(r) and b(r) are extracted? I assume it's trivial, but somehow I don't see it. Thanks.
