Anmerkungen:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments April 16, 2023 erstellt
Beschreibung:
We derive closed form analytic formulas for European vanilla options in the driftless Oscillating Brownian Motion model defined by two semi-infinite regimes each with its own constant local volatility. In particular we solve the Ito and Stratonovich Fokker-Planck equations for the probability density using Fourier cosine transform. The density functions are slightly different but they both have a finite discontinuity where the local volatility jumps, which is a well-known result in multi-layer diffusion problems. What is not known however, to the best of our knowledge, that the Ito density can be integrated with the vanilla payoff in closed form and yields vanilla prices expressible with the Bachelier option price formula. Finally, we show the normal implied volatility is bounded by the levels of the local volatility and is continuously differentiable across the regime boundary