Put-Call Parity

The prices of call and put options are related via the put-call parity theorem. This important relationship obviates the need for a separate model for put options. 

Consider two portfolios, Y and Z. Y consists of a call option with a maturity date T and a zero-coupon bond that pays out Xon T Z consists of a put option also maturing on date T and one unit of the underlying asset. The values of portfolios Y and Z on the expiry date are given by equations (8.24) and (8.25), respectively. 

Both portfolios have the same value at maturity. Since prices are assumed to be arbitrage free, the two sets of holdings must also have the same initial value at start time t. The put-call relationship expressed in (8.26) must therefore hold. 

From this relationship it is possible to construct equation (8.27) to derive the value of a European put option. 

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There is a similar put-call parity for European options contingent on a discount bond. If Pp(0, t) Tq-,k he price at r = 0 of a European put option on the discount bond with maturity T, then for B(0) = 1,... 

Put-call parity can be used to derive the price of a European put option... 

Use the put-call parity theorem to calculate the price of the put option, pluming in the call price derived above 4.3303. The put-call parity equation is... 

The figure on the following page shows the spreadsheet formulas required to build the Black-Scholes model in Microsoft Excel. The Analysis Tool-Pak add-in must be available, otherwise some of the function references may not work. Setting up the cells in the way shown enables the fair value of a vanilla call or put option to be calculated. The latter calculation employs the put-call parity theorem. 

Klemkosky, R., and B. Resnick. 1979. Put-Call Parity and Market Efficiency. 

The total parity of a given class of levels (F fine structure component for E-states, upper versus lower A-doublet component for II-states) is found to alternate with 7. The second type of label, often loosely called the e// symmetry, factors out this (—l) 7 or (—l)-7-1/2 7-dependence (Brown et al., 1975) and becomes a rotation-independent label. (Note that e/f is not the parity of the symmetrized nonrotating molecule ASE) basis function. In fact, for half-integer S, it is not possible to construct eigenfunctions of crv in the form [ A, S, E) —A, S, — E)], because, for half-integer S, vice versa.) The third type of parity label arises when crv is allowed to operate only on the spatial coordinates of all electrons, resulting in a classification of A = 0 states according to their intrinsic E+ or E- symmetry. Only A = 0) basis functions have an intrinsic parity of this last type because, unlike A > 0) functions, they cannot be put into [ A) — A)] symmetrized form. The peculiarity of this E symmetry is underlined by the fact that the selection rule for spin-orbit perturbations (see Section 3.4.1) is E+ <-> E, whereas for all types of electronic states and all... 

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