Dividend Timing in the European Put Lower Bound

Summary

The document questions how a cash dividend should enter a European put’s lower-bound formula when it is paid before maturity. It compares the stated bound, which adds the dividend without discounting, with a proposed version that discounts the dividend from its payment date to the present while discounting the strike from maturity.

The author frames the issue through a portfolio comparison: a put combined with the underlying is compared with an investment intended to reproduce cash flows at the dividend date and at maturity. The document does not provide a resolution or supporting calculation, so it is best read as a clearly posed question about cash-flow timing rather than a complete derivation. Its formulas assume a known dividend amount and payment date; further assumptions about rates and the underlying’s dividend treatment would be needed to establish the precise bound.

Key ideas

• The question concerns the timing of a known dividend in a European put lower bound.
• The proposed adjustment discounts the dividend from its payment date and the strike from option maturity.
• The portfolio argument compares cash flows at both the dividend date and maturity.
• The document raises the issue but does not resolve it or give a full derivation.

Tags

# Why not discount the dividend in the european put lower bound condition?


# Why not discount the dividend in the european put lower bound condition?












According to the european put lower bound condition:

$ p \geq max(D + K \cdot e^{-r(t_2-t_0)} - S_0, 0)$

where $t_0$ is now and $t_2$ is maturity. Say $t_1$ is the dividend release time where $t_0<t_1<t_2$.

Shouldn't it be:

$ p \geq max(D \cdot e^{-r(t_1-t_0)} + K \cdot e^{-r(t_2-t_0)} - S_0, 0)$ ?

The common proof when it comes to portfolio B consists of investing $D + K \cdot e^{-r(t_2-t_0)}$ at the risk-free rate. (Portfolio A is going long on a put and the asset. The 2 portfolios' cashflows are compared and it is shown that since $P_A \geq P_B$ at $t_2$ that should stand for $t_0$ as well.)

Shouldn't we invest instead:

$D \cdot e^{-r(t_1-t_0)} + K \cdot e^{-r(t_2-t_0)}$ in order to get equal cashflows $(=D)$ at time $t_1$? I.e. discounting the divident in the same fashion with the strike but at its respective time-frame?

I struggle to get my head around this, thank you!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.