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...