Ibrahim Nasser Khatatbeh
May, 2013

Q1: Explain how the option pricing formula developed by black and scholes can be used for common stock and bond valuation. Include in your discussion the consequences of using variance applied over the option instead of actual variance.

Its generally known that Black and Scholes model became a standard in option pricing methods , with almost everything from corporate liabilities and debt instruments can be viewed as option (except some complicated instruments), we can modify the fundamental formula in order to fit the specifications of the instrument that will be valued.
An argument done by Black and Scholes which was based on the past proposition of Miller and Modigliani a well as assuming some ideal conditions, States that value of the firm is a sum of total value of debt plus the total value of common stock. As well as the fact that in the absence of taxes, the value of the firm is independent of its leverage and the change of debt has no effect on the firm value.
V = E + Dm
V: value of the firm.
E: shareholders right (common stock values).
Dm: market value of the debt.

As the above equation impose that Equity (common stock values) can be viewed as a call option on the firm value (due to the shareholders limited liability and with consideration that firm debt can be represent as a zero-coupon bond), where exercising the option means that equity holders buy the firm at the face value of debt (which is in this case will be the exercise price of the option), on the liquidation date of the bond (maturity).
The equity value can be represented as the option on the value of the firm (as the remaining after closing the debt on the expiration date) which is limited by the following boundaries:
From the above equation the value of equity at the expiration date will be …. ET =