A Risk Neutral Framework For The Pricing Of Credit Derivatives :: Business Finance Essays

A Risk Neutral Framework For The Pricing Of Credit Derivatives 1. INTRODUCTION Considerable research effort has gone into Credit Derivatives since the early 1990’s. The roots of credit derivatives can be traced back to the notion that the credit risk of a firm can be captured by the credit rating ascribed to it. This premise is also the cornerstone of loan pricing and credit risk management models the world over, including J.P. Morgan’s CreditMetricsTM. Empirical research enables the predictability of the event of default as well as the Loss in the Event of Default (LIED). This information is expressed in terms of a ‘transition matrix’ - a matrix that traces out the probabilities the migration of a firm’s credit rating. Rating agencies such as Standard & Poor (S&P) provide transition matrices computed from periods of data about bonds - default record and post-default behaviour in the US markets. Lack of adequate data precludes the computation of such matrices in the Indian context, although it is possible to map ratings of Indian rating agencies such as CRISIL onto S&P ratings. 2. TYPES OF CREDIT DERIVATIVES Here is a brief description of some popular types of credit derivatives: 2.1 Credit Default Swaps A credit default swap provides a hedge against default on some payment, such as a bond. The counterparty buying credit protection pays the provider a certain amount in return for a guarantee to make good the loss in the event of default. 2.2 Total Return Swaps In this contract, the ‘payer’ gives a ‘receiver’ the total return on an asset in return for the returns on a benchmark asset, typically a risk-free asset. The payer has thus eliminated the risk of default in return for a lower but certain risk-free rate of return. 2.3 Credit Spread Derivatives Credit spread derivatives take the form of credit spread options, forwards or swaps. A credit spread call option, for example, is a call option written on the level of the spreads for a given bond. The option, thus increases in value as the spread increases, so that the value of the bond is protected. 3. RISK-NEUTRALITY Hypothesising the existence of a ‘risk-neutral’ world is extremely useful in the pricing of instruments whose value is derived from a stochastic process. In the real world, the present price is less than the expected net present value of the likely outcomes in future. Thus, for example, if the price of a commodity can become either Rs.