Finite Difference Techniques for Arbitrage Free SABR

This paper presents various finite difference schemes applied to the SABR arbitrage free density problem. Hagan initially proposed a Crank-Nicolson discretization, which can lead to oscillations in the option price. Among a variety of finite difference schemes, it is found that the TR-BDF2 and Lawson-Swayne schemes stand out on this problem in terms of stability and speed.

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