Suppose that the spread between the yield on a 3-year...

Suppose that the spread between the yield on a 3-year zero-coupon riskless bond and a 3-year zero-coupon bond issued by a corporation is $1 \%$. By how much does BlackScholes-Merton overstate the value of a 3-year European option sold by the corporation.

Key Concepts

Black-Scholes-Merton Model

The Black-Scholes-Merton model is a widely used framework for pricing European options. It assumes the underlying asset follows a continuous process and that markets are free of arbitrage, with parameters such as volatility and risk-free rate. However, it does not account for credit risk, which can lead to overvaluation when pricing options issued by risky corporations.

Yield Spread

The yield spread is the difference between the yield on a riskless bond and that on a risky corporate bond. It reflects the additional return investors demand over the risk-free rate as compensation for taking on credit risk and other uncertainties associated with the corporate issuer.

Credit Risk

Credit risk is the possibility that a corporation will default on its obligations. In the context of bond yields and option pricing, credit risk affects the discount rates applied to cash flows from the corporate bond issuer, thereby influencing the valuation of derivatives such as options.

Risk-Neutral Valuation

Risk-neutral valuation is a pricing framework where the expected returns on all assets are discounted at the risk-free rate. When applied to corporate securities, ignoring the credit risk inherent in the yield spread can lead to mispricing. For corporate options, using a risk-free discount rate may overstate the option’s value since it does not incorporate the higher implied discount rate due to default risk.

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