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Negative Rates, Settlement Cash Flows, and Shadow Pricing

Article Quant Q&A · Author: user7056
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Summary

The document asks whether negative interest rates require separate pricing models for electronic and physical cash flows. It proposes treating physical settlements as observed portfolio cash flows, discounting outgoing and incoming amounts using portfolio-specific funding and investment rates, and considering the timing and size of non-electronic flows. Treasury rates are suggested as possible proxies for those rates.

The response rejects the need to explain negative-yield bonds through a split between software and physical money. Instead, it points to shadow pricing: an interest rate may sit below the opportunity cost of funds when desired borrowing or investment returns differ from the quoted rate. The response notes that settlement methods, frequency, and amounts can enter portfolio asset-liability management. No pricing formula or empirical evidence is supplied, so the proposed cash-flow framework remains unvalidated in this exchange.

Key ideas

  • The question proposes separate treatment of electronic and physical settlement cash flows.
  • Funding and investment rates could be estimated from the portfolio’s incoming and outgoing physical flows.
  • Shadow pricing can explain why observed interest rates may differ from the opportunity cost of funds.
  • Settlement method, frequency, and cash-flow size may matter in portfolio asset-liability management.
  • The exchange provides no formula or empirical test of the proposed modeling approach.

Tags

Fixed incomeRisk managementPortfolio construction
Full text
# Separated software and physical cash flows modelling and pricing to be used with negative interest rates?


# Separated software and physical cash flows modelling and pricing to be used with negative interest rates?












The physical cash presence in the final transactions is one of the issues in the presently observed negative interest rates bonds. Such a situation has historically been modelled within the "liquidity trap" theory, forecasting the introducing of a unique plasma currency in order to solve inflational problems. But currently one is observing both electronic-trading /credit cards/checks based- (software-) and physical money flows, with country-specific interchange rates.

In the present netting system an additional netting is therefore showing up: the one of software cash flows. From the perspective of limited monetary mass, all the pricing instruments should have different formulae for the software and non-software settlement. The evolution of interest rates allowing for negative values need to be portfolio-specific and modeled taking into account not only the time, but also the frequency and the magnitude of the overall non-software flows.

Would, in your opinion, dedicated pricing and modelling of the two different forms of cash flows make a difference?

I thought of seeing this extra netting in place, from the portfolio's owner point of view, by having the physical flows considered as observed values. The negatives (outgoing principals) will be discounted at the effective funding rate (the by-principal-weighted average of all the incoming/positive non-software flows) and the positives (deposited) should be discounted at the average opportunity of investing rate (the weighted-by-principal return rate of all the non-software future flows). The treasury's rates (where they exist) might be taken as a proxy for effective funding and opportunity of investing rates when calculating present value of non-software cash flows. This might be treated as a technical detail of what to do if differentiating the two, so not necessarily within this topic.

## Answer by user7056 (score 1, accepted)

https://quant.stackexchange.com/a/4062

No. The shadow pricing of goods theory can explain the presently observed negative interest rates bonds. A shadow interest rate shows when the expected return is greater than interest rate (as firms wish to borrow more at given interest rate than they can) and opportunity cost of funds is greater than interest rate.

Considering two additional ulimate local nettings (over the software- and physical-money) at the level of the modelled portfolio, the treasury department does the asset versus liability management. Frequency, magnitude, settlement methods do get involved in such a modelling.

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.