We define long shots as investment projects with four features: (1) low probabilities of success; (2) long gestation lags before any cash flows are realized; (3) large required up-front investments; and (4) very large payoffs (relative to initial investment) in the unlikely event of success....

The 2007-2009 financial crisis has led legislators on both sides of the Atlantic to propose laws that would require most “standardised” over-the-counter (OTC) derivatives to be cleared centrally. This paper examines these proposals. Although OTC derivatives did not cause the crisis, they do...

A feature of credit markets is the large difference between probabilities of default calculated from historical data and probabilities of default implied from bond prices (or from credit default swaps). This paper illustrates and discusses the reasons for the difference between historical and...

Traditionally practitioners have used LIBOR and LIBOR-swap rates as proxies for risk-free rates when valuing derivatives. This practice has been called into question by the credit crisis that started in 2007. Many banks now consider that overnight indexed swap (OIS) rates should be used as the...

A company's credit default swap spread is the cost per annum for protection against a default by the company. In this paper we analyze data on credit default swap spreads collected by a credit derivatives broker. We first examine the relationship between credit default spreads and bond yields...

Regulatory changes are increasing the importance of collateral agreements and credit issues in over-the-counter derivatives transactions. This paper considers the nature of derivatives collateral agreements and examines the impact of collateral agreements, two-sided credit risk, funding costs,...

This paper shows how reinforcement learning can be used to derive optimal hedging strategies for derivatives when there are transaction costs. The paper illustrates the approach by showing the difference between using delta hedging and optimal hedging for a short position in a call option when...

In 1976 Black and Cox proposed a structural model where an obligor defaults when the value of its assets hits a certain barrier. In 2001 Zhou showed how the model can be extended to two obligors whose assets are correlated. In this paper we show how the model can be extended to a large number of...

Researchers such as Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) have proposed a one-factor model for asset prices that is exactly consistent with all European option prices. In this model, which we refer to as the implied volatility function (IVF) model, the asset price...