Counterparty Funding Costs and Derivative Valuation Differences

# Risky funding rates and unique price


# Risky funding rates and unique price












I have a very basic question about risk neutral pricing with funding costs. For example, in Piterbarg (2010), he introduces a modified version of Black--Scholes and shows that when there is no, or incomplete collateral, the fair value can depend on the funding rate $r_f$ which is going to vary between counterparties, depending on their credit-worthiness.

This means different counterparties to the same derivative deal can see a different "price" if they have different funding rates. I don't understand what this means and how to reconcile this with traditional no-arbitrage frameworks where we assume a unique risk-free rate is used everywhere leading to a unique price in the market.

This point does not seem to be mentioned at all in that paper or in any other places so I am clearly completely missing something. I don't understand how this framework is useful in practice if it leads to market participants having different views of the fair value of the same deal. Is someone able to help with the fundamental misunderstanding that I clearly have? Thanks.

## Answer by Greg (score 5)

https://quant.stackexchange.com/a/82258

You’ve spotted a paradox. Yes, in Piterbarg’s framework, counterparties with different funding rates can value the same derivative differently, which seems to go against traditional no-arbitrage principles.

This is because the traditional framework assumes perfect markets with a single risk-free rate available to all. Piterbarg’s model acknowledges the post-crisis reality: different institutions have different funding costs, especially for uncollateralized or partially collateralized trades.

These different valuations don’t violate no-arbitrage principles because:

The funding cost differences are real economic frictions that can’t be arbitraged away without taking on additional risk (mainly credit risk).

When a derivative is fully collateralized, everyone values it the same (discounted at the collateral rate). Differences only emerge for uncollateralized parts, where each party has to consider their own funding cost.

In practice, the market handles this through competitive dynamics. Trades execute near prices offered by well-funded dealers, while other participants internally adjust valuations to reflect their funding costs.

Think of funding costs as an institution-specific “tax” on derivative positions rather than a mispricing. If Bank A funds at 3% and Bank B at 5%, Bank A can’t arbitrage this difference because any attempt to do so would create unhedged credit exposure.

This is why modern accounting standards require recognition of Funding Valuation Adjustment (FVA) - it’s a real economic cost that varies between counterparties.

The framework is still useful in practice because it accounts for real-world frictions not present in classical theory, so institutions can measure their true economic costs and profitability when entering into derivative transactions.