In this paper, I study risk-neutral probability densities regarding future Libor rates denominated in British pounds, euros, and US dollars as implied by option prices. I apply Breeden and Litzenberger's (1978) result regarding the relationship between option prices and implied probabilities for...

We propose a method to extract individual firms' risk-neutral return distributions by combining options and credit default swaps (CDS). Options provide information about the central part of the distribution, and CDS anchor the left tail. Jointly, options and CDS span the intermediate part of the...

Background: We investigated the determination of the pledged loan-to-value ratio in an optionpricing environment and mainly articulated the theoretical framework and analytical method. Methods: The basic idea is that the present value of the pledged loan payoff is equal to a put option’s...

The yield on the 10-year U.S. Treasury Note is among the most cited interest rates by investors, policymakers, and fnancial institutions. We show that the 10-year Treasury yield's forward-looking volatility, a VIX-style measure that is a proxy for uncertainty about future interest rates, is a...