We show that the optimal stopping boundary for the Russian option with finite horizon can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation (an explicit formula for the arbitrage-free price in terms of the optimal stopping boundary having a clear economic interpretation). The results obtained stand in a complete parallel with the best known results on the American put option with finite horizon. The key argument in the proof relies upon a local time-space formula.
Keywords:Russian option finite horizon arbitrage-free price optimal stopping smooth-fit geometric Brownian motion free-boundary problem nonlinear integral equation local time-space calculus curved boundary
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