A put spread collar option requires its holder to sell an asset at the price \(f(S)\) when its market price is at the level \(S\), where \(f(S)\) is the function plotted in Figure 3.10, with \(K_{1}:=80, K_{2}:=90\), and \(K_{3}:=110\).

a) Draw the payoff function of the put spread collar as a function of the underlying asset price at maturity.

b) Show that this put spread collar option can be realized by purchasing and/or issuing standard European call and put options with strike prices to be specified.
Hints: Recall that an option with payoff \(\phi\left(S_{N}ight)\) is priced \((1+r)^{-N} \mathbb{E}^{*}\left[\phi\left(S_{N}ight)ight]\) at time 0 . The payoff of the European call (resp. put) option with strike price \(K\) is \(\left(S_{N}-Kight)^{+}\), resp. \(\left(K-S_{N}ight)^{+}\).

Transcribed Image Text:

130 120 110 100 90 80 70 60 Put spread collar price map f(S) y=S 70 90 K Figure 3.10: Put spread collar price map. 80 K SN 100 110 K3 120 130