Show that a portfolio long in an asset-or-nothing call option (Exercise 11) and short in a cash-or-nothing call option with cash K (Exercise 10) has the same time-n value as a portfolio with a long...

Show that a portfolio long in an asset-or-nothing call option (Exercise 11) and short in a cash-or-nothing call option with cash K (Exercise 10) has the same time-n value as a portfolio with a long position in a call option with strike price K.

Exercise 10

(Cash-or-nothing call option). Let A be a fixed amount of cash. Show that the cost V0 of a claim with payoff A1(K,∞)(SN ) is

where m is defined as in Theorem 7.3.3.