Abstract
The SABR models are very popular in the financial industry. Their evaluation using asymptotic formulas for implied volatilities is fast and widely used but becomes less accurate and exhibits negative probability distribution values around zero strikes for long maturities. In addition, alternative version for more accurate valuation exists but involves numerical integration. In this paper, we apply the homotopy analysis method (HAM) to derive approximated option prices under a SABR model. This scheme is simple and our numerical examples demonstrate that the derived price can be evaluated easily and gives a good approximation with a computational cost that is only several times heavier than that of the Black-Scholes model. We also discuss the application of HAM to XVA evaluation.
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