Hi

@sohinichowdhury I really like your question (because I love financial philosophy)! The law of one price says that absent confounding factors (e.g., credit risk is a big one), there is only a single discount factor at each maturity. This is my expression but it is equivalent to Tuckman's definition:

"This reasoning is an application of the law of one price: absent confounding factors (e.g., liquidity, financing, taxes, credit risk), identical sets of cash flows should sell for the same price." -- Tuckman, Bruce; Serrat, Angel. Fixed Income Securities: Tools for Today's Markets (Wiley Finance) (p. 55). Wiley. Kindle Edition.

Let me briefly illustrate. But we will assume we are referring to the riskfree term structure (i.e., no credit risk) and my interest rate is too high but that's only to make comparisons easier. Let's say that one-year riskfree rate is 5.00% per annum with semi-annual compounding. If that is the case, then the one-year discount factor is, d(1.0) = 1/(1+0.050/2)^2 = 0.9518144. Consequently, the

**only correct **theoretical price for the one-year (riskfree) bond is $95.18144.

It is a violation of the law of one price to assume that, additionally, the one-year riskfree rate is 5.00% per annum with quarterly compounding. That interest rate implies a different discount factor; 0.9515243. This demonstrates that 5.00% per annum is

**insufficient **to specify an interest rate!

Instead, if the one-year discount factor is 0.9518144, then we can infer per [($100.00/$95.18144)^(1/4)-1]*4 = 4.96913% that the correct one year rate is also 4.96913% per annum with quarterly compounding. Or for that matter, the correct one year rate is ln(100/95.18144) = 4.9385% per annum with continuous compounding.

The law of one price says each maturity has only one discount factor, which is the same as saying that (in this case) a one-year zero-coupon bond can only have one price (!), but this implies a different stated (aka, nominal) rate for each different compound frequency. I'm not sure quite how to untangle you application, but hopefully that's enough guidance to apply. Thanks,

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