Implied Dynamics in the SV-HJM Framework
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In this chapter we apply the ACE methodology developed for the generic term structure (TS) framework in Chap. 5. We focus on very liquid interest rates derivatives products, valued within a universal Stochastic-Volatility (SV) Heath-Jarrow-Morton (HJM) modelling setup. Our aim is still to link the underlying’s instantaneous (stochastic volatility) dynamics to the shape and dynamics of the implied volatility surface, with a natural emphasis on the direct problem (from model to smile) and on the first layer (second order in strike and first order in maturity). Thanks to the results provided in the generic framework, this application can be performed in only two steps. The first is rather conceptual and involves casting each product type (bond options, caplets, swaptions) into the generic framework, by allocating several TS (the underlying, the numeraire, the measure and the payoff). The second step is more computational and consists in computing the chaos dynamics for the underlying TS defined above, within the chosen SV-HJM parametrisation.
KeywordsTerm Structure Yield Curve Stochastic Volatility Implied Volatility Martingale Measure
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