The condition known as "put-call parity" restricts the relationships 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 the 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:

Vt = Et + Dt

where, at any such date t, Vt denotes the market value of the property, & 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. The Modigliani-Miller proposition is simply a re-interpretation of the put call parity condition but allowing for risky debt. Below vou need to state how the terms in the Modigliani and Miller proposition translate to the respective terms for asset value, put option, call option and a riskless zero-coupon bond, Vt, Pt, Ct and Bt in the statement of put-call parity ₁

i.) What term or terms in the Modigliani-Miller condition correspond to the underlying asset value V in put-call parity?

ii.) What term or terms in the Modigliani-Miller condition correspond to the call option C in put-call parity?

iii.) What term or terms in the Modigliani-Miller condition correspond to the remaining term or terms in put-call parity?

b. Using your answers in (a), what is the difference between riskless and risky debt?

c. Based on your answer to (b), to what term in the Modigliani-Miller condition, as based on the put-call parity condition, does "credit risk" correspond?

d. Does the borrower or lender pay for credit risk?

 

₁ Recall that, in the put-call parity condition, the underlying asset is often interpreted as a share of stock in finance textbooks. Moreover, the put and call options have a common exercise price, the riskless zero coupon bond has a face value equal to this common exercise price, and that future values of all the terms are discounted at the riskless rate.