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Suppose in the following portfolios all options are based on the same stock, have expiry date $T$ and strike price $K$ (unless otherwise stated). In each case find the portfolio value at time $T$ in terms of $S_T , K$:

  1. one call option and one put option;

  2. two call options and one share sold (i.e. short);

  3. one share, short one call option;

  4. one $(K_1,T)$ call option, short one $(K_2,T)$ put option.

For the first portfolio, I got $$\max(K-S_T,S_T-K)$$

For the second portfolio, I have $$\max(2(S_T - K),0)-S_0$$

For the last two I am really unsure and would be happy about your help.

Community
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KingDingeling
  • 1,642

1 Answers1

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For portfolio 3:

$$(S_T-S_0) - max(S_T - K,0)$$

For portfolio 4: $$ max(S_T-K_1,0) - max(K_2-S_T,0)$$

Also, I believe Portfolio 2 should be: $$max(2(S_T - K),0)-(S_T-S_0)$$

Also, all of these valuations ignore any financing benefit/costs.

AlRacoon
  • 691