Joint Forward Curve and Volatility Surface Models for Swaption Hedging

Summary

The document frames a model-selection problem for reinforcement-learning-based dynamic hedging of long-dated swaptions. The proposed application uses 2y2y and 4y2y swaptions, requiring simulated paths that update both a forward swap curve and an implied volatility surface as positions roll and moneyness changes. The desired model should produce a full curve and surface at each simulation step while maintaining no-arbitrage consistency.

The author considers Cheyette, SABR-LMM, and a co-terminal Swap Market Bergomi model. They raise questions about whether the latter fits a setting involving different swap tenors, and whether the first two provide suitable evolving state variables rather than primarily supporting Monte Carlo pricing. The document poses these as unresolved modeling concerns; it presents no model comparison, calibration evidence, or recommendation, so it is best read as a statement of requirements and open questions rather than a validated solution.

Key ideas

• Dynamic swaption hedging requires joint evolution of the forward curve and implied volatility surface.
• Rolling swaption positions cause their moneyness and relevant points on the surface to change over time.
• The author seeks simulation steps that generate a full curve and surface while preserving no-arbitrage consistency.
• Cheyette, SABR-LMM, and co-terminal Swap Market Bergomi are considered, but their suitability is left unresolved.

Tags

# What model(s) can be used to simulate the joint dynamics of the 2y forward curve and implied volatility surface?


# What model(s) can be used to simulate the joint dynamics of the 2y forward curve and implied volatility surface?












I am trying to train a reinforcement learning model for dynamic hedging like Cao et al. 2023. Their model uses SABR to generate joint dynamics of implied volatility and underlying equity asset prices.

I want to use their deep hedging framework with 2y2y and 4y2y swaptions for hedging instead of equity options. For this I will need both the volatility surface as well as the full forward curve, as the swaption positions roll and the moneyness changes over time.

I am stuck as to what model should be used for joint dynamics of the 2y forward swap curve and the volatility surface. I am interested in a model that for each Euler step gives a full forward curve, as well as a volatility surface, both evolving dynamically with no arbitrage.

I have been looking at everything from the Cheyette model to SABR-LMM, as well as the Co-terminal Swap Market Bergomi Model, however it models co-terminal swaps, and im not sure if it can be applied in my case. For the first two models mentioned, im not sure that they are concerned with accurate state spaces as much as they are used for pricing with Monte Carlo.

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