Question

Provide a detailed proof showing that the Put-Call parity can be used to characterize the capital structure of a company.

Answer 1

How put call option parity design capital structure of the company:

The pioneers of option pricing namely Fisher, Scholes, Robert Merton, it was these people who showed in the early 1970’s itself that options can be used to characterize the capital structure of the company.

For example, consider a company whose assets comprise of zero coupon bonds and equity. If the bonds maturity happens at the end of five years with principal payment of k, the company doesn’t pay any dividends. If the value of the assets is more than k at the end of five years, then equity holders will repay the bond holders. But if the assets are less than k, then equity holders will decline bankruptcy and bond holders become the owners of the company.

The value of equity at the end of five years is (Ar – K, 0) where Ar is the value of the assets. This can prove that equity holders have a five-year European call option on the assets of the company with t strike price of k. in case of bond holders they get min (Ar, k) in five years. This is equal to k – max (k- Ar, 0). This shows that value of k minus value of five year European put option on the assets with strike price of k.

Thus if c & p are the values of call and put options, then:

Value of equity = c

Value of company’s debt – PV(K) – p

The value of assets must be equal t the instruments that is used to finance the assets. In that case,

Ar = c+(PV(k) – p)

Consolidating the equation:

C+ PV(k) = p+AR

This proves that put call parity influence the company’s assets.