On Option Greeks and Corporate Finance

Abstract

This paper has proposed new option Greeks and new upper and lower bounds for European and American options. It also shows that because of the put-call parity, the Greeks of put and call options are interconnected and should be shown simultaneously. In terms of the theory of the firm, it is found that both the Black-Scholes-Merton and the binomial option pricing models implicitly assume that maximizing the market value of the firm is not equivalent to maximizing the equity-holders’ wealth. The binomial option pricing model implicitly assumes that further increasing (decreasing) the promised payment to debt-holders affects neither the speed of decreasing (increasing) in the equity nor the speed of increasing (decreasing) in the insurance for the promised payment. The Black-Scholes-Merton option pricing model, on the other hand, implicitly assumes that further increasing (decreasing) in the promised payment to debt-holders will: (1) decrease (increase) the speed of decreasing (increasing) in the equity though bounded by upper and lower bounds, and (2) increase (decrease) the speed of increasing (decreasing) in the insurance though bounded by upper and lower bounds. The paper also extends the put-call parity to include senior debt and convertible bond. It is found that when the promised payment to debt-holders is approaching the market value of the firm and the risk-free interest rate is small, both the owner of the equity and the owner of the insurance will be more reluctant to liquidate the firm. The lower bound for the risky debt is: the promised payment to debt-holders is greater or equal to the market value of the firm times one plus the risk-free interest rate.