Applying the Law of One Price to Assets with Interim Cash Flows
Summary
The document asks how to apply the law of one price to two bonds with the same maturity and maturity payoff when one bond also pays coupons before maturity. The question highlights that matching only the final payoff does not make the two investment cash-flow streams identical: coupon payments create value at earlier dates. It also asks how the proposition’s reference to a time point should be understood for instruments with interim or exercise-related cash flows.
The response clarifies that equality should be considered at each relevant time between the present and maturity, not only at maturity. In the example, the coupon-bearing and zero-coupon bonds differ at intermediate dates because the coupons have already been paid by one instrument. The short exchange offers a useful distinction between terminal payoff equivalence and equality of cash flows through time, but it does not give a formal theorem or discuss how to price reinvested coupons or contingent exercise rights in detail.
Key ideas
- Matching terminal payoffs alone does not establish equality of instruments with interim payments.
- Coupon-bearing and zero-coupon bonds have different cash flows before maturity.
- The law of one price comparison must account for relevant intermediate times.
- For instruments with flexible exercise, equality may need to hold across possible exercise dates.
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# Basic question/clarification about the LOOP
# Basic question/clarification about the LOOP
This is a very basic question/comment regarding the way that the LOOP is stated in the book "Dan Stefanica - A Primer for the Mathematics of Financial Engineering". The proposition goes as follows:
What confuses me is that there is no restriction on the number of dividends paid by these portfolios at any time $t < \tau$ prior to maturity.
Indeed:
- let $V_{1}$ be a coupon-bearing bond and
- let $V_{2}$ be a zero-coupon bond,
both with same maturity and same payoff/value at maturity. The LOOP can't be true if $V_{1}$ has non-zero coupon payments at $t < \tau$. Should this additional restriction be added or is there something that I'm missing? Thanks in advance!
EDIT:
I’m looking for an elaborate answer on why would the author say that the statement holds only assuming the existence of one $\tau$. I guess that the author is thinking of the V’s as instruments that have only one payoff at a fixed time (like european options or forwards). If that is not the case, (V is an american option, for example) then I guess that the equality of the portfolios should be required on all $\tau$’s between $t$ and maturity.
## Answer by phdstudent (score 2)
https://quant.stackexchange.com/a/74721
You are missing something, you should interpret $\tau$ as every point in time from $t$ to maturity (in the case of your example). Clearly your statement only holds true for $\tau = maturity$. In any point in time such that $t < \tau < maturity$ the portfolio of the zero coupon bond and the coupon bearing bond will be different.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.