The condition known as "put-call parity" restricts the relationship between the value of an asset, put and call options written on that asset, and the value of a riskless (zero-coupon) bond with a face value equal to the common exercise price of the corresponding call and put options. This condition is not only fundamental to the pricing of options, but also to understanding the relationship between the value of a leveraged asset and equity and debt claims on that asset. A famous proposition in financial economics, proffered by the economists Modigliani and Miller, essentially restates put-call parity in the following terms: "In an efficient set of financial markets, the following equality is always satisfied at any date t:

V_t = E_t + D_t

where, at any such date t, V_t denotes the market value of the property, E denotes the market value of the equity claim on that property, and D denotes the market value of the corresponding value of the risky mortgage (debt claim) on that property.

a) How do the terms V_t, E_t and D_t in the Modigliani and Miller proposition translate to the terms V_t,

P_t, C_t, and B_t in the statement of put-call parity.

b) Can you define, under the conditions assumed by Modigliani and Miller, the value of risky debt in terms of the value of riskless debt and at least one other term in the put-call parity expression? What term or terms are those?

c) Can you use your answers above to verbally interpret the relation between risky and riskless debt? Can you also interpret the value of credit risk? How about the value of the option to default on the mortgage?