Adapting Monte Carlo Pricing Architecture to Swaptions
Summary
The discussion considers how to adapt an equity Black–Scholes Monte Carlo framework, built around product definitions and simulation timelines, to price interest-rate swaptions. The suggested shortcut is to represent the underlying swap rate as a forward-like variable with Black–Scholes dynamics and reuse a European option payoff. This is a way to fit the existing architecture, rather than a full model of the rates that determine swap values.
A more direct extension would define swap rates as simulated rate variables and add a product with a swaption-specific payoff. The answer points to an implementation using a Vasicek model as an example of this approach. It does not provide derivations, validation results, or details on calibration and rate-curve construction, so it serves as architectural guidance rather than a complete pricing recipe. It also notes that extending a general simulation framework can require more expertise than the phrase “easily extended” suggests.
Key ideas
- A Monte Carlo product framework can describe when market variables are simulated and which variables are needed.
- A swap rate can be treated as a forward-like underlying under Black–Scholes dynamics to reuse a European option implementation.
- A more direct approach simulates rate variables and defines a swaption-specific payoff.
- A Vasicek-based simulation is cited as an example, but the discussion gives no pricing validation or calibration details.
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# Antoine Savine code proposition and swaptions # Antoine Savine code proposition and swaptions I am reading Antoine Savine's book "Modern Computational Finance: AAD and Parallel Simulation" and exploring is code proposition at the same time. Basically for him products (he doesn't speak about payoffs because he wants to keep it simple) have deflines and timelimes : he is exclusively in a Monte-Carlo pricing setting and the timelime of a product tells times at which market variables needed to evaluate the product and simulated in the pricing model have to be simulated, and the defline tell what has to be simulated, roughly. He tells that his setup could be easily adjusted for making it cover pure rates products, like swaptions, but I cannot wrap my mind around it and see how. He has an equity Black-Scholes model and I would like to use it, even if it is stupid, to diffuse short rates, and price swaption like this, but I don't see how. His general architecture is here : https://github.com/asavine/CompFinance/blob/master/mcBase.h while concrete implementations are here : https://github.com/asavine/CompFinance/blob/master/mcMdlBS.h (Black-Scholes Model) https://github.com/asavine/CompFinance/blob/master/mcPrd.h (european option) Help would be greatly appreciated. ## Answer by Landscape (score 1) https://quant.stackexchange.com/a/79984 I based parts of my masters thesis on a simulation engine inspired by the one presented in Antoine’s book. If you wish to you the European call and Black Scholes Class then you are essentially considering the underlying swap of the swaption as what he calls “forwards” which has a stochastic dynamic under the Black Scholes model (as opposed to any of the rates). Essentially this is “forcing” your approach onto the Classes. Alternatively, you could extend the code in several ways. For instance by using a struct similar to the RateDef for (forward) swap rates and creating another product where you alter the payoff function to be that of an swaption. In my thesis, we used this approach with the Vasicek model. Check out the Python Code here for the simulation and try to also navigate to the Vasicek model and Swaption product which are imported in the script: https://github.com/KennoCapital/CenterfoldCapital/blob/main/application/experiments/vasicek/unit_tests/vasicek_mc_european_swaption. It should perhaps also be noted that when Antoine writes “easily extended” you should keep in mind that Antoine is among some of the top quants in the world.
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