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I'm trying to improve my understanding of valuation under collateralisation.

One point that is made within multiple sources is for an uncollateralised derivative, how a future cashflow is equivalent to a loan made to that counterparty, and how the holder of the derivative must take that loan.

I just can't see this equivalence. If we were to 'convert' or 'realise' a future cashflow to a present cashflow (to, for example, pay salaries or some other cost), then we would have to go out and borrow some amount, with the repayment of that principle plus interest to be made by that future cashflow (the basic present value arbitrage reasoning). So we discount the future value by whatever the cost of funding is. Nowhere is there a relationship with the derivative counterparty. Further, I can't see how there is a mandatory requirement to take this loan.

Is there a simple perspective that I have missed that would resolve my confusion?

Some examples:

How to hedge the fixed leg of a swap contract?

Assume the swap is not collateralized, then you have to fund all future values. The net payments in the swap are then payed by corresponding the maturing of the corresponding funding contracts (which you created dynamically in your hedge).

(why do we have to fund anything?)

Collateral replication argument

Let us consider the situation where the firm A has a positive present value (PV) in the contract with the firm B with high credit quality. From the view point of the firm A, it is equivalent to providing a loan to the counterparty B with the principal equal to its PV. Since the firm A has to wait for the payment from the firm B until the maturity of the contract, it is clear that A has to finance its loan and hence the funding cost should be reflected in the pricing of the contract. (again, why does firm A has to finance anything)

https://vdoc.pub/documents/the-xva-of-financial-derivatives-cva-dva-and-fva-explained-ruskbvi6ess0

they are effectively unsecured borrowing and lending with the counterparty

https://www.pwc.com.au/pdf/xva-explained.pdf

Similarly, a funding cost arises for the bank when a derivative has a positive market value. The purchase of an ‘in the money’ or asset position derivative requires the bank to pay cash. The incremental cost of funding this purchase can also be seen as equivalent to the cost of the bank raising funding.

I can understand why a bank would need to fund if they were to purchase an in the money derivative, but why does there need to be any funding for a derivative that starts with zero valuation and then goes into the money?

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When we say that holding an uncollateralized derivative is equivalent to taking a loan from the counterparty, we are referring to the economic exposure and funding implications associated with the derivative contract. The key point is that the derivative contract represents an agreement between two parties to exchange future cash flows based on the underlying asset or reference rate.

In an uncollateralized derivative, there is a credit risk associated with the counterparty's ability to meet its obligations. The party holding the derivative is exposed to potential losses if the counterparty defaults. To mitigate this risk, the holder of the derivative needs to consider the potential funding cost associated with the exposure.

To put it in perspective, consider the following scenario:

  1. You enter into an uncollateralized derivative contract with Counterparty A.
  2. Over the life of the contract, the derivative generates positive cash flows for you, which you expect to receive from Counterparty A at various future dates.
  3. However, as a prudent risk management practice, you need to consider the possibility that Counterparty A may default or fail to meet its obligations. This introduces a credit risk.
  4. To protect yourself against the credit risk, you would need to set aside or reserve some funds or capital to cover potential losses in case Counterparty A defaults.
  5. This setting aside of funds or capital can be seen as an implicit loan made to Counterparty A. You are effectively lending them the amount required to cover the potential losses.
  6. The funding cost arises because you need to obtain the funds to cover this potential exposure. You may need to borrow or raise capital to finance this loan-like exposure.

So, the concept of funding arises from the need to protect against the credit risk associated with uncollateralized derivatives. It is not a direct loan transaction with the counterparty, but rather an implicit funding requirement to cover potential losses.

It's important to note that in collateralized derivatives, the collateral acts as a form of protection against counterparty default risk, reducing the need for explicit funding. The collateral serves as a buffer to cover potential losses, and the holder of the derivative can utilize the collateral to offset their exposure.

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  • $\begingroup$ Thanks @toureiffel! I’ve been trying to parse your response to see if I can use it to resolve my issue. I’m not quite there on why we need to set aside funds. Is there some sort of risk equivalence angle that explains this (I.e something like the setting aside of funds results in a definite cash flow irrespective of default)? I hadn’t considered that this was related to credit risk so your answer is definitely helpful and feels like it’s on the right path for me to answer my question. $\endgroup$
    – Trent Di
    May 31, 2023 at 22:53
  • $\begingroup$ Setting aside of funds or capital is a way of managing this risk. If the counterparty defaults, you will suffer a loss. To cover this potential loss, you need to set aside some funds. By setting aside funds, you are ensuring a certain cash flow to cover potential losses, irrespective of whether the counterparty defaults or not. This effectively reduces the credit risk of the derivative, bringing it closer to a risk-free state This set-aside of funds is a cost, similar to the cost of taking a loan. You are giving up the opportunity to use these funds elsewhere. @TrentDi $\endgroup$
    – TourEiffel
    Jun 1, 2023 at 7:55
  • $\begingroup$ @TrentDi You can think of the setting aside of funds as a way to 'de-risk' the derivative, making its cash flows more certain, much like a risk-free asset. Because if the derivative is uncollateralized, there is the risk that the counterparty could default, which introduces uncertainty or risk into those future cash flows. This risk is the 'credit risk'. $\endgroup$
    – TourEiffel
    Jun 1, 2023 at 7:56
  • $\begingroup$ @TrentDi To compensate for this risk, one needs to take into account the potential loss from default. This is done by adjusting the discount rate used to calculate the present value of the future cash flows. This adjusted discount rate is generally higher than the risk-free rate, reflecting the additional risk. Therefore, the present value of the future cash flows (i.e., the value of the derivative) will be lower when you consider the possibility of default. Setting aside of funds or capital is a way of managing this risk. $\endgroup$
    – TourEiffel
    Jun 1, 2023 at 7:59
  • $\begingroup$ Thanks @TourEiffel. For some reason it's still not making 100% sense in my brain. I will ponder it and get back to this answer! $\endgroup$
    – Trent Di
    Jun 14, 2023 at 10:54

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