Abstract
We consider the problem of how to price and hedge derivatives on underlyings that trade on exchanges with no overlap in opening hours. For a simple two-stock model we derive the dynamics of closing prices, show how they can be simulated efficiently and what value we should put into pricing formulae for a non-observable stock. We then use utility maximisation to show that the price can still be approximated with the 2-stock version of the Black-Scholes PDE and derive expressions for the optimal delta hedges, which are path-dependent but can be written as the ideal delta hedge plus a proxy hedge for the untradable stock.
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