Function BPV within with keys - also known as DV01 - returns the Basis Point Value(s) of the referenced bond(s) as of a given reference date Tˢ
It equals the change in NPV dP caused by an increase in yield by one basis point.
Obtained by setting dy = 0.0001 in the following 2nd-order Taylor series expansion.
dP = delta*dy + ½*gamma*(dy)²
The coefficients delta, gamma are computed as follows:
delta = -D*P, where D is the bond's modified duration
gamma = C*P/100, where C is the bond's convexity
If the settlement date Tˢ is not explicitly given, it will be set to the bond's settlement date as implied by a trade transaction assumed to occur on the T₀ (typically today).
PRECAUTION: This function treats the referenced bond as if it were a fixed rate bond even if this is not the case!
All index-linked cash flows are treated as fixed cash flows that pay the amount forecasted by the corresponding curve.