Replication in Derivatives

CFA Level II Derivatives
#21

Hi @S2000magician , are you able to help me understand the following?

  • A replication portfolio for a call option consists of a leveraged position in h shares where h is the hedge ratio or delta of the option
  • A replication portfolio for a put option consists of a long position in a risk-free bond and a short position in h shares.

I’m struggling to place the above in the context of the put-call parity

Thanks!

#22

Am I right in thinking you use replication portfolios in binomial trees, so you only have 2 states (up and down)?
Let’s do an example:
call with strike 50 and initial stock price 50 and up price of 60 and down price of 40
replicate with hS-Ae^{-rt}
S=40 need payoff=0
S=60 need payoff=10
so replicating portfolio is S/2-20e^{-rt}

put with strike 50 and initial stock price 50 and up price of 60 and down price of 40
replicate with -hS+Be^{-rt}
S=60 need payoff=0
S=40 need payoff=10
so replicating portfolio is -S/2+30e^{-rt}

Call - put =S-50e^{-rt} which is exactly put-call parity