Modeling Yield Curve Spread Options for Pricing and Vega Hedging

Summary

The document frames a modeling choice for yield curve spread options. One approach focuses on the payoff at expiry: model the marginal distributions of the two rates and connect them with a copula to represent dependence. The alternative considers the needs of a dynamic vega hedge, where both underlying rates and changes in vanilla option sensitivities may matter over time.

It raises the possibility that hedge rebalancing costs should affect the option’s value and asks whether that makes a path-dependent volatility model more appropriate. The document gives no answer, model specification, pricing comparison, or empirical evidence, so it presents an open modeling question rather than a recommendation. Its central distinction is between matching the terminal joint distribution and representing the evolution relevant to hedging; the appropriate choice depends on the product and hedging objective.

Key ideas

• A terminal-payoff approach can model the two rate marginals and use a copula for their dependence.
• Dynamic vega hedging may require modeling both underlyings over time.
• Changes in vanilla option sensitivities can affect hedge rebalancing needs.
• The document asks whether hedging costs justify a path-dependent volatility model but does not resolve the question.

Tags

# Pricing/Hedging a yield curve spread option (YCS)


# Pricing/Hedging a yield curve spread option (YCS)












I have 2 perspectives as to what model to use for a YCS option:

- It is an at the expiry option, so hit the marginals, correlate them with a copula, and be done with it.

- To hedge the vega, I will need to have both underlyings. Moreover, I might need to rebalance the hedge in the future (say rates move, I lose/gain vega sensitivity on vanillas so I have to buy less/more of them). This should ideally be priced in the YCS (price should have some component of hedging costs), so I should probably regard this as a path dependent product and use a stock vol model.

Any advice as to which one is correct? Thanks!

Edit: I suppose this concern applies to any multivariate at the expiry payoff.

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