ABSTRACT

FIGURE 6.2: Probability density p(K,T |f0) = ∂ 2C(T,K) ∂2K . Asymptotic so-

lution vs numerical solution (PDE solver). The Hagan-al formula has been plotted to see the impact of the mean-reverting term. Here f0 is a swap spot and α has been fixed such that the Black volatility αfβ−10 = 30%.