This paper shows that the standard textbook formula for computing the present value of a future random cash flow – the discounted expected value – is formally incorrect and can generate significant errors when used to compute present values. The correct present value method is provided as...

In economic theory, both discrete and continuous time models are commonly believed to be equivalent in the sense that one can always be used to approximate the other, or equivalently, any phenomena present in one is also present in the other. This common belief is misguided. Both (strict) local...

Loan commitments represent more than 82 percent of all commercial and industrial loans by domestic banks. This paper develops a valuation model for loan commitments incorporating early exercise, multiple fees, partial exercise and credit risk. The model is analytically tractable and easy to...

This note provides a simple closed form solution for valuing Cat bonds. The formula is consistent with any arbitrage-free model for the evolution of the Libor term structure of interest rates. The crucial inputs to the valuation formula are the likelihood of the catastrophe event, per unit time,...

This note shows how to hedge in a HJM model when the term structure evolution is Markov in the entire forward rate curve.

Unconventional monetary policy tools are based on the belief that there exists a zero-lower bound on interest rates. This paper argues, based on economic theory and the empirical evidence, that this belief is a myth and not a reality. It is shown that a negative default-free spot rate of...

There are two competing paradigms for modeling credit risk: the structural and reduced form models. This paper applies our knowledge of credit market equilibrium to this debate. We show that credit markets have asymmetric information in the borrowing and lending relationship which influence...

The purpose of this paper is to clarify the risks of leveraged ETFs. We do this by showing how to construct a k-times leveraged ETF as a dynamic portfolio in the ETF and a money market account. This construction characterizes the return distribution of the leveraged ETF over any investment...

This paper provides a model for housing prices based on a seller solving the optimal time-on-the market problem. Given the seller’s optimal time-on-the market, analytical expressions are provided for both the expected time-on-the-market and the sales price. These expressions facilitate the...