Learning Curve

Demand and supply fix the prices of traded assets in every market. The prices are taken as given and plain-vanilla derivatives traders view them through the Black-Scholes model to derive implied volatilities. The role of the quants is to create models that are consistent with market data. These models are based on parameters that are local and the task is to make sure the implied parameters by the model match the implied parameters from the market. This is a guarantee of a low model error. The Dupire model as it is explained in [1] is an illustration of a model that uses local volatility to price consistently with European prices or implied volatilities.

The use of sophisticated risk management tools is being rapidly adopted in the investment management industry. We view this trend as natural given that asset managers are in the business of taking risk. In other words, whether their mandate is to fund contingent liabilities, such as pension funds, produce excess returns over a benchmark, such as traditional asset managers, or generate exceptional absolute returns, such as hedge funds, asset managers need to assume risk in order to meet their objectives.

Roulette wheels have been adding value to casino owners in Monte Carlo for hundreds of years, but more recently the mathematical technique named after that city--also used in quantum physics and atomic bomb research--has found a valuable application in finance. This Learning Curve looks at one simple application of Monte Carlo analysis to calculate the risk that LIBOR will exceed a set level in a given period of time. This allows the risk of a floating-rate investment to be quantified and helps to answer questions such as:

Much of the considerable growth of the credit derivatives market has been driven by the use of the default swap as a proxy for cash instruments. This is predicated upon the assumption that a default swap and a par floater or asset swap (on a par asset) closely replicate the same credit exposure. However this relationship is not exact and this is reflected in the market where we observe that significant divergence can occur between default swap and cash spreads. We call this spread divergence the default-swap basis and define it as follows:

To benefit from the next bull-run, investors are on the lookout for the bottom of the market. Historically speaking, an upward trend has nearly always followed major shocks, such as the Cuban Missile crisis, JFK's assassination, the Kuwait invasion and the Russian crisis. It is possible that the trend over next year may also be upwards as major central banks cut interest rates and most countries implement fiscal easing policies in the aftermath of the Sept. 11 attacks. However, many analysts believe that further dips in the equity markets and continued high volatility may be seen next year before the upward trend becomes obvious.

Credit-default swaps are well established in the debt market as hedging instruments against credit risk and to enable market participants to establish a synthetic short position in a specific reference credit and implement credit-trading strategies outside the cash markets. The most common method of pricing default swaps is by recourse to the asset-swap spread of the reference credit, as the default-swap premium should, in theory, be equal to the asset-swap spread of the reference asset. We first consider the use of this technique, before looking at the issues arising that cause these two spread levels to differ.

The generation of large, positive semi-definite covariance matrices that properly reflect market conditions has been a challenge for finance practitioners for several years. Since the 1996 amendment to the 1988 Basel accord, where the principals of internal models for the calculation of market-risk capital were outlined, it has been a major problem to generate the covariance matrices that are necessary to calculate firm-wide Value at Risk estimates. In very large portfolios a risk factor model may be employed, but it is still necessary to have a covariance matrix for all the risk factors of the portfolio.

There have been major changes to accounting standards in Japan which, by the time they have all been implemented will have brought Japanese accounting standards broadly into line with international norms. These changes are comprehensive and include the introduction of fair value--or mark-to-market--accounting. This last change, although seemingly innocuous will be particularly powerful in its impact.

Deutsche Bank and J.P. Morgan, which are going to start offering derivatives based on economic statistics (DW, 10/29), will employ new technology and intellectual property called Parimutuel Digital Call Auction (PDCA) technology, developed by Longitude, to create the derivatives.

In the U.K. and several other major markets, reverse convertibles, high coupon products financed by a short put option, have been popular in the retail investment arena. Investors are ever hungry for income, dissatisfied with meagre returns from deposit accounts, and have turned in a big way to stock market-linked high income bonds in the last three years. These investments usually have a fixed maturity of between one and five years and pay interest well above risk-free yields - typically 8-11% p.a.. While the income is fixed and guaranteed, the capital is not and is linked to one or more equity indices or stocks. In order for the capital to be repaid in full the equity performance must reach a certain target, for example not falling over the lifetime of the bond.

Traditionally collateralized debt obligations (CDOs) involve a transfer of collateral assets. The CDO liabilities then reference the cash flows (principal and interest) of the collateral assets. But CDOs are increasingly issued in synthetic form, where there is no physical transfer of collateral. In these structures the CDO references default losses, rather than the cash flows of the referenced collateral.

The Institute of Certified Public Accountants of Singapore approved an accounting standard for derivatives similar to the ones introduced by the Financial Accounting Standards 133 in the U.S. and the International Accounting Standards 39. The statement was passed in July 2000 to become effective for financial periods beginning on or after July 2001.