Comparing SABR, Short-Rate, and Libor Market Models
Summary
This document outlines trade-offs among three interest-rate option model families. It describes SABR as a formula-based approach used for European swaptions and some foreign-exchange vanilla options, with efficient computation and established hedging practice, but limited to terminal-style products. Short-rate models such as Hull–White and Vasicek can handle Bermudan structures and are computationally efficient, though the described versions have limited ability to represent volatility skew and curve-twist dynamics. The post characterizes Libor Market Models as suited to American and Bermudan products because they represent Libor market dynamics, correlations, and caplet volatility.
The comparison also flags limitations: LMM extensions are needed for skew, and Monte Carlo simulation can make pricing costly; short-rate models may allow negative rates and often suit near-the-money products; SABR's distribution can have boundary issues. These are broad, dated forum notes rather than a complete survey or benchmark. The author frames the list as an initial comparison and asks whether other models should be included.
Key ideas
- SABR is presented as an efficient formula-based choice for European swaptions and some vanilla FX options.
- The described SABR setup is aimed at terminal products rather than Bermudan options.
- Short-rate models can support Bermudan pricing but may represent skew and curve dynamics poorly.
- LMM captures market dynamics and correlations but can require costly Monte Carlo pricing.
- The model trade-offs depend on product structure and the volatility behavior that must be represented.
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# Comparison of Option-Pricing Models (volatility models) vs Product-Mapping # Comparison of Option-Pricing Models (volatility models) vs Product-Mapping I scoured this forum, looking for some indicative (updated as of year 2021) comparison of volatility/option-pricing models. There were some, but they seem dispersed and lacking in general details... Are there any good papers/forums where there is a good summary? Not looking for anything exhaustive, but along the lines of pros/cons/limitations. For example, I found this : https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2272823 ... but it's back in 2013 (and won't have been adapted to recent changes).... I'll start, for example - Replication/Terminal Distribution SABR The default pricing-model for European Swaptions, both in Interest-Rate and somewhat in FX Vanilla Options. Standard variation now (2022) is on a zero-shift, lognormal OR a bachelier Normal-distribution model. Pros : easy implementation; decomposed into Formula-based; well-understood and 'hedged' by traders, efficient computation. Cons : only for terminal products (no Bermudanality), Zero-bound failure in pdf (probability distribution -> but solved using zero-shift) - Short-rate Models (Hull-White or Vasicek). Seldom-used now, except for simplistic Bermudan-style options with close-to-ATM strike options Pros : Can be used for Bermudan products; can be decomposed into Formula-based; efficient computation. Cons : Only one parameter for volatility-skew (i.e. cannot capture vol-skew), mainly for ATM products then; Hull-White can have negative rates; cannot replicate curve-twist dynamics unless adding more factors - Libor Market-Models (LMM) Default model mainly used for American-style and/or Bermudan-style products Pros : Able to describe complete market-dynamics per the Libor markets -> correlation, caplet vols Cons : Need extension to volatility, to capture vol-skew; computationally expensive, can only use Monte-Carlo; Cannot be formula based to easily price (European Swaptions) and efficient computation. The above are what I have... Did I miss anything? Kind regards (to all the Option experts/Quants out there!)
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