On Option Greeks and Corporate Finance
This paper has proposed new option Greeks and new upper and lower bounds for European and American options. It 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 equityholders’ wealth. The binomial option pricing model implicitly assumes that further increasing (decreasing) the promised payment to debtholders 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 implicitly assumes that further increasing (decreasing) in the promised payment to debtholders 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 specifies the lower bound for risky debt and the conditions under which American put option will not be early exercised.
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