Derivatives help economy – Greenspan



THE Wall Street Journal of May 9-11 2003 quotes the Federal Reserve chairman Alan Greenspan as saying “the use of financial derivatives to manage risk has been a stabilising factor underpinning the US economy”.
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He argued that financial market participants, including banks, who purchased derivatives, had spread their risks and helped to lessen the severity of the 2001 recession. Derivatives essentially are contracts whose value depends on an underlying asset, which in turn could be anything, such as commodities, currency, interest rates, equities or equity indices.


The derivative market in Zimbabwe had grown considerably from $100 million in 2001 to approximately a $1 billion by March 2003, while the number of institutions trading has increased from one to five over the same period. These figures are small compared to the estimated value of unregulated derivatives market of US$3 trillion in 1990, which had since grown to US$127 trillion by the end of 2002 in US markets.


In our view the benefits of derivatives far exceed their cost, largely because of their hedging ability. The Derivatives Association of Zimbabwe (DAZ) has often touted the benefits of derivatives in stabilising the economy and efforts by the Zimbabwe Stock Exchange to try and regulate and bring some order to the over-the-counter derivative market signifies a positive development to our nervous economy and must be welcomed. The stabilising effect of derivative instruments was also noticed on the ZSE between November 2002 and March 2003.


Below, we give an account of the trading and operational risk management techniques adopted in derivatives trading to show how they bring stability in the economy.

* “The writer” assumes minimal price risk on all its option contracts. Therefore all option posi-tions are hedged by the appropriate, corresponding position in the underlying asset. The traders/dealers are not allowed to take any naked positions.


Details of the hedging techniques applied are outlined below:


* When the call option position is created, the quantity of the underlying securities purchased is as per a 1:1 hedge ratio, ie one share covers one position. However, this hedge ratio is varied as the price of the underlying security fluctuates. The appropriate hedge ratio is determined by the computed delta of the option position, as per the adjusted Black and Scholes formula used to price the call option positions, details of which are well documented in various literature.

* Positions are marked to market on a per call-over basis, with risk monitoring occurring before each day’s sales and trading, between call-overs, and at the end of each trading day. The risk monitoring and assessment methodology is a one-day day 95% value at risk (VAR) model adjusted for option gamma.

* The trade or dealer can set the desk’s overall sale and trading limit, say Z$X notional, ie the underlying notional book value of all the outstanding option contracts shall not exceed Z$X under any circumstances.

* All option sales with a notional value exceeding a certain preset limit must be approved by both the relevant authorities responsible for the operations of the desk and there-fore are given a time allowance for confirmation.

* On dealing with liquidity problem in some counters, rules may be set, for example, that all option sales on counters whose average daily trading volumes are below Y shares must be approved by the authorities put in place by the writer, and therefore are given a time allowance for confirmation.

* To mitigate losses, tolerant limits can also be set, so much that if losses exceeding a certain amount are to be sustained within a time period, trading is to be suspended for a time period, after which a risk management meeting must be convened to decide on whether trading should continue or cease.


Market risk management

* We measure the sensitivity of the options value to movements in the price of the underlying asset using its delta. This is computed as the first derivative of the adjusted Black and Scholes Model, and represents the hedge ratio that is to be maintained, that is in the event that the writer is not necessarily using the one-to-one hedge ratio. The hedge ratio is to be adjusted twice a week in line with the computed theoretical option delta. All contracts are to be delta hedged via the underlying security, such that the overall delay of each position shall be zero.

* We measure the sensitivity of the option delta to changes in the option price using its gamma, computed as the second derivative of the Black and Scholes Model. The large the option gamma, the more frequent is the rebalancing of the option portfolio to achieve delta neutrality. Gamma neutrality, which ensures insensitivity to large price changes, may be achieved by purchasing options from other counter parties. It is also important to track the theta, which measures the sensitivity of the option position to the passage of time. This does not need to be hedged against.

* The value at risk (VAR) methodology is used overall to track global risk on a daily basis, on the basis of the 95% confidence level. The return distribution is modelled by the daily returns over the past trading year and adjusted for the option gamma as given by (2) above. The VAR for the overall options desk should not exceed 3,5% of the notional outstanding on any given day, i.e. maximum losses are not expected to exceed $3,5 million with a probability of 95% on any given day. In the event that it does, the portfolio is to be rebalance appropriately at the next call-over


Pricing

* The quoted option prices are based on an adjusted Black and Scholes Model, with appropriate modifications for dividends. The pseudo American call value is then computed as the highest European call option price for early exercise scenario.