After the Fed raised target interest rate in March 2022, the portfolio manager in Signora Capital believes that a turmoil in the equity market will come soon. She expects that the volatility of the S&P 500 index will rise in the near future and considers an option strategy to make a profit from the increase in the market volatility. Ideally, the strategy is only exposed to changes in the implied volatility and is immune to changes in the S&P 500 index. You immediately come up with the following three candidate strategies: Long straddle: Long 1 call option with strike price K and long 1 put option with strike price K. Long strangle: Long 1 call option with strike price K2 and long 1 put option with strike price K1 (K1 < K2).

Short call butterfly: Short 1 call option with strike price K1, long 2 call options with strike price K2, and short 1 call option with strike price K3 (K1 < K2 < K3 and 2K2 = K1 + K3).

 

Our colleague tells you that the short butterfly strategy can also be implemented using only put options (short put butterfly): short 1 put option with strike price K1, long 2 put options with strike price K2, and short 1 put option with strike price K3 where K1 < K2 < K3 and 2K2 = K1 + K3. Assuming no bid-ask spread or transaction cost, does the short call butterfly and the short put butterfly have the same initial cost? Prove your claim.

Answer rating: 100% (QA)

Yes the short call butterfly and the short put butterfly have the same initial cost assuming no bidask spread or transaction costs Heres why 1 Symmetr... View the full answer