Ratchet Floater Pricing - 2023.2 English

Vitis Libraries

Release Date
2023.2 English

A ratchet floater is a path dependent interest rate product. This option is a good example for the use of the LIBOR market model, since no analytic formula exists. At each time \(T_i, i > 0\), the ratchet pays a coupon amount \(c_i\). The ratchet floater price is the sum of all coupons.

For a ratchet floater with notional \(N\), constant spreads \(X\) and \(Y\) and fixed cap \(\alpha\) the price can be calculated with:

\[RFloater = \sum_{i=0}^{n}(N(\tau_i(L_i(T_i) + X) - c_i)\frac{B(0)}{B(i+1)})\]
\[c_i = c_{i-1} + min\{(\tau_i(L_i(T_i) + Y) - c_{i_1})^+, \alpha\}\]
\[c_1 = \tau_1(L_1(T_1) + Y)\]
\[B(t) = [\prod_{k=t}^{n}(1+\tau_kL_k(t))]^{-1}\]

This means that the coupon \(c_i\) is at least as much as the previous coupon amount, but no more than the previous coupon plus a fixed constant \(N\alpha\)