call option

call option

For Questions assume all options are European style with maturity T.A‘K call’ is call option with strike price K. A ‘knockout’ option has payout zero if the defined event occurs.
Butterflies, condors and call ladders
(a) Recall that a call butterfly with strikes (K1, K1 + β, K1 + 2β), for some fixed β > 0, is a portfolio consisting of +1 K1 call, +1 (K1 + 2β) call and –2 (K1 + β)
calls. Using put-call parity or otherwise, restate the call butterfly as a portfolio consisting solely of puts. (b) A callcondor is a portfolio consisting of +1 K call, –1 (K + β) call, –1 (K + 2β) call and +1 (K + 3β) call. Draw the payout of the condor, and express the condor as a portfolio consisting solely of call butterflies. (c) A call ladder consists of +1 K call, –1 (K + β) call and –1 (K + 2β) call. What relationships hold between the prices at time t ≤ T of the call ladder, butterfly and condor with common maturity T?