Model-free valuation of barrier options
Austing and Li provide a continuous barrier options pricing formula that fits the volatility smile
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Peter Austing and Yuan Li provide an analytic formula for valuing continuous barrier options. The model exactly fits the implied volatility smile in a manifestly arbitrage-free way and produces prices consistent with an underlying stochastic volatility dynamic
The standard approach to valuing continuous barrier options, developed in the literature by Jex (1999) and Lipton (2002), is to use a local stochastic volatility (LSV) model. Such models begin with an
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