put-call symmetry

By put-call symmetry we understand the relationship (see [2], [3],[5] and [6])

$\begin{displaymath} v(x,K,T,t,\sigma,r_d,r_f,+1)=\frac{K}{f}v(x,\frac{f^2}{K},T,t,\sigma,r_d,r_f,-1). \end{displaymath}$

(32)

The strike of the put and the strike of the call result in a geometric mean equal to the forward

. The forward can be interpreted as a geometric mirror reflecting a call into a certain number of puts. Note that for at-the-money options (

) the put-call symmetry coincides with the special case of the put-call parity where the call and the put have the same value.

2000-06-11