Black vs Bachelier Caplet Pricing

Compare lognormal vs normal models — and watch Black break for negative forwards

\(\text{Caplet} = N\Delta\,Z(0,T_{i+1})\cdot \text{Model}(f, r_K, \sigma, T_i)\)

Strike \(r_K\) 3.00%

Selected forward \(f\) 3.50%

Black vol \(\sigma_f\) (rel.) 25%

Bachelier vol (bp) 100 bp

Expiry \(T_i\) 1.0y

Discount factor \(Z(0,T_{i+1})\) 0.97

Black requires \(f > 0\). Bachelier handles all values.

Black price

Bachelier price

Intrinsic value

Black − Bachelier
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