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I'm working with put/call options for a finance class, and am having just a little bit of confusion with the formulae. For call options, I know that the formula to determine price (C(0)) is equivalent to C(t) = $\left(\frac{s^u - p_c}{s^u-s^d}\right)$ * s(t) - $s^d$ $\left(\frac{B(t)}{B(1)}\right)$ where t = 0, of course.

I know that put options are very similar, but instead of being given the option of buying the asset, the owner is given the option to sell (at the 'strike price') at a given date. Thus, I'm thinking that the two formula are very similar, however we have not been taught in class what it was, and I was curious.

Any help would be greatly appreciated!

user3472798
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  • Hint: Put-Call Parity tells us that being long the call and short the put at the same strike is equivalent to the forward purchase at that price. – lulu Nov 30 '15 at 00:06
  • @lulu Would this imply that they both use the same formula? I'm new to the short/long terms (and with this concept) – user3472798 Nov 30 '15 at 00:27
  • Not at all. By parity, the price of the put less the price of the call equals the present value of the forward purchase at the strike. Hence $P(0)-C(0)=PV(K-F)$ Where F is the forward price (probably just LIBOR on top of the spot price in your case). Does that make sense? – lulu Nov 30 '15 at 00:30
  • Should say: "parity" here is really just common sense. If you are long the call at $K$ and short the put at $K$ then in all scenarios you end up owning the asset at $K$ when the options expire. – lulu Nov 30 '15 at 00:32
  • @lulu and what is 'K' standing for in this case? – user3472798 Nov 30 '15 at 00:40
  • $K$ is the strike. If $K$ equals the forward price, then the price of the call and the put coincide, not otherwise. Maybe worth pointing out that the beauty of put-call parity is that it is model independent. In particular, it is true regardless of whatever underlying process you imagine that your asset price will follow. Of course, the explicit pricing formulas depend on the underlying model. – lulu Nov 30 '15 at 00:42
  • @lulu gotcha, sorry for my ignorance, I'm incredibly new to this. When you say PV(K-F), is this just equivalent to K-F, or do I need to use a present value formula? – user3472798 Nov 30 '15 at 00:47
  • PV means "present value", you'll need to discount (presumably at LIBOR). – lulu Nov 30 '15 at 00:48

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