A local vol model calibrated to today's surface prices every vanilla option correctly. It fails at something subtler: it predicts wrong forward smiles — that is, wrong implied vol surfaces at future dates, conditional on the path of the spot. The failure is not about fitting; it is about dynamics. This matters enormously for any exotic option whose price depends on how the smile moves when the spot moves — barrier options, cliquets, forward-starting options, autocallables.
This note establishes the forward smile problem precisely, shows why local vol predicts a smile that collapses to flat as the spot moves, and explains why this is the opposite of what market data shows. The consequence is the central critique of pure local vol and the motivation for stochastic local vol (SLV) hybrids.
Learning objectives. By the end of this note you should be able to:
- define the forward smile and the forward-starting smile formally;
- state local vol's prediction for the smile's movement under spot shifts and contrast it with sticky-delta;
- explain why local vol produces the "wrong" forward smile for cliquets and barrier options;
- describe qualitatively how a stochastic-local-vol hybrid remedies the problem.
In this lesson
- 4.1 The forward smile
- 4.2 Local vol's prediction: the smile flattens
- 4.3 The consequence for exotic pricing
- 4.4 The stochastic-local-vol hybrid — qualitative overview
Before you start
- Pricing in the Local Vol Model — PDE and Monte Carlo
- Reading the Implied Vol Surface — Moneyness, Term Structure, and Quoting Conventions
The full lesson, with worked examples and exercise solutions, is for members.
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