Why Risk-Neutral and Real-World Values Match at Today’s Mark

Summary

The document asks why interest-rate derivative exposure profiles simulated under risk-neutral and real-world probabilities can have the same value at the valuation date even though their future paths differ. Its brief answer attributes the equality to marking the trade to its current market value on that date. The question also raises how drift and volatility choices affect projected exposure under the two probability measures.

The explanation is only a concise assertion and does not develop the pricing argument. In general, a traded derivative’s current market value is a price calibrated to market data, while the probability measure and drift used for future simulations depend on the purpose of the profile. Equality at the starting date does not imply that future exposure distributions match. The document gives no model specification, numerical example, or discussion of valuation adjustments, so its answer should be treated as a starting point rather than a full account of counterparty credit risk modelling.

Key ideas

• The question concerns exposure profiles under risk-neutral and real-world measures.
• Both profiles are stated to begin at the trade’s current market value.
• Different drift assumptions can produce different future exposure paths.
• The short answer does not explain calibration or modelling details.

Tags

# No arbitrage principle in Counterparty Credit Risk


# No arbitrage principle in Counterparty Credit Risk












I think this is a fairly basic question but I'm struggling to understand the no-arbitrage principle applied to CCR.

Imagine that we want to calculate the exposure evolution in an IR derivative, comparing risk-neutral vs real-world probabilities. We will have two different profiles that have the same value on the day of today due to the no-arbitrage principle.

Why are both valuations equal? Is it because both are considering the current market value of the trade, and as time goes by, the evolution is different depending on the way the drift and volatility parameters are calculated? If it is not due to the current market value, how are the parameters of the pricers adjusted to have the same result?

Many thanks,

## Answer by smriti (score 0)

https://quant.stackexchange.com/a/80818

The valuation are equal under both physical and risk neutral measure due to MtM of trade to today's date.

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