Pricing Unilateral Extinguishers with Path-Dependent Credit Events

Summary

A unilateral extinguisher is a swap portfolio that may be canceled after a credit event affecting one counterparty. Whether it ends depends on whether its mark-to-market value is above a contractually set threshold; a recovery payment may also apply. This makes the payoff depend on both the credit event and the portfolio value at that time.

The response contrasts this structure with a zero-recovery bilateral extinguisher, for which a closed-form pricer is described as straightforward. It says Monte Carlo is the only known approach to pricing the unilateral version, particularly when recovery can depend on time and other parameters. The example clarifies why a simple label such as “derivative” does not imply a tractable analytic formula. It does not provide a derivation, implementation details, or evidence comparing pricing methods, and it does not establish that Monte Carlo is the only possible method in general.

Key ideas

• A unilateral extinguisher can cancel a swap portfolio after a credit event if its mark-to-market exceeds a specified threshold.
• The payoff may include recovery, which can depend on portfolio value, time, and other parameters.
• A zero-recovery bilateral extinguisher is presented as having a straightforward closed-form pricer.
• The response identifies Monte Carlo as the known approach for the more complex unilateral structure, without proving that no alternatives exist.

Tags

# Derivatives without analytic expressions?


# Derivatives without analytic expressions?












I was wondering if there exist options or other derivatives that do not have a known closed-form analytic expression (i.e., some sort of Black-Scholes PDE) and are usually priced using Monte Carlo methods, but that could have such an expression? Specifically, I am wondering if it is possible to analyze the price data of some derivative as a function of time and underlying price to discover a PDE using something like symbolic regression or other ML-based techniques?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/75711

A unilateral extinguisher is a simple example, as it is easy to describe.

Counterparties A and B have a portfolio of swaps between them, e.g. interest rate swaps or cross-currency swaps. For similicity, you can even consider just one swap. For simplicity, assume no margin, collateral, or netting agreements.

The portfolio has some mark to market value V.

If CDS-like credit event happens to credit C then: if V>v for some contractually specified strike v, then the portfolio "extinguishes", i.e. all the swaps in the portfolio are canceled, but some recovery may be paid out. Else the portfolio lives on.

In practice, the recovery could depend not only on V, but on the time and other non-trivial parameters.

It is easy to write a closed-form pricer for a zero-recovery bilateral extinguisher, which just extinguishes with no recovery irrespective of the value of V. But I am not aware of a methodology other than MC to price a unilateral one.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.