PUT – CALL PARITY Sample Clauses

PUT – CALL PARITY. Put-Call Parity Formula The premiums of a European call and a European with the same underlying stock and the same characteristics satisfy an important relation called put-call parity. Three versions of this relationship are stated below. • General Put-Call Parity. C ( K , T ) − P ( K , T ) = PV ( F0,T ) − PV ( K ) 0, T C ( K , T ) − P ( K , T ) = F P − PV ( K ) • Put-Call Parity for Non-Dividend Stock: C ( K , T ) − P ( K , T ) = S 0 − PV ( K ) Note that the put-call parity relationship only holds for European options. The derivation for the put-call parity relation can be found in the FM notes. We will reproduce it here, but it would be useful to review. It is important to note that the parity relation must hold regardless of the model used to price the options.
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PUT – CALL PARITY. For European options, there is a fixed relationship between the price of put and call options with the same maturity and written on the same underlying security. Recall: S + P = B + C or S + P - B = C. Consider the combination, S + P - B; Buy one share of stock (+S0), buy one put (+P), and sell a bond (-B) for E/(1+R), maturing at expiration. Cash Flows Value at Expiration Portfolio Today If S1>E If S1<E Portfolio A (buy synthetic call): buy stock -S0 S1 S1 buy put sell bond -P +E/(1+R) 0 -E E-S1 -E Total: -S0 - P + E/(1+R) S1-E 0 Portfolio B (buy call): -C S1-E 0 Outcomes are identical. Thus, initial cost of Portfolio A must be same as call: -C = -S0 - P + E/(1+R) C = S0 + P - E/(1+R) Put-Call Parity.
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