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Suppose That the Asset Value of a Firm Evolves According

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Suppose that the asset value of a firm evolves according to a lognormal diffusion, as in Merton (1974) . The current value of the firm's assets is $100 million, and its volatility is 24.24%. Suppose too that the firm has only one issue of debt outstanding: zero-coupon debt with a maturity of three years, and a face value of $70 million. Finally, suppose that the risk-free rate of interest is 4% (continuously-compounded terms) for all maturities. What is the risk-neutral probability of the firm defaulting at maturity of the debt?


Definitions:

Selling Price

The amount of money a buyer pays to purchase a product or service.

Call Option Contract

A financial contract that gives the buyer the right, but not the obligation, to buy an asset at a specified price within a specific timeframe.

Underlying Asset

The financial asset upon which a derivative instrument, such as an option or a futures contract, is based.

Floating-Rate Debt

Floating-rate debt is a type of loan or security that has a variable interest rate, which adjusts periodically based on a benchmark or index rate.

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