Contingency Risk and Policy Issues

Contingency risk means that the risk is linked to a certain trigger. Options do fit here, as you could sell the option to give something in case something else happens. Financial options are also linked to an underlying transaction that triggers changes in the option value, which is why options and futures are called derivatives.

Options

Options as financial instruments, allow for contingent risk to be traded. They started in 1973 when the Chicago Board Options Exchange was born. 1977 put options (the right to sell a security) were introduced. Within 10 years the value of options traded exceeded that of the underlying shares. Then more underlying were added and more financial centers. There are four main types of options: on shares, on interest rates, on currencies and on commodities.

A call options allows you to buy x shares at price y at date z. A put option allows you to sell x shares at price y at date z. American options can be exercised on or before expiry and european options on the expiry date.

Quotations telll you for example:

C&W 460 Jan/50

this would mean that for 500 pounds, you can buy an options for 1000 C&W shares for a price of 460p up till the third wednesday in January. If at that time, or before, the C&W share price is at 510p a share, then buying them for 460p will give you a profit of 50px1000= 500 pounds, meaning that you came out even. Above that price you made a profit.

There is always a buyer and a seller/writer wiith options. Writers could be pension funds or asset management companies that want to hedge.

A call option with the exercise price below the current share price is called in the money, with the money gained being the intrinsic value. With the EP below the share price, it is called out of the money. With EP=SP it is called at the money. If the option price is above the intrinsic value of the option, this difference is called the time value, meaning what one would pay because of belief that the shares could rise. With the time to expiry shrinking, time value also shrinks.

As options give you the right but no obligation to excercise that very option, the loss is limited to the price of the option, making them important for portfolio insurance and guaranteed funds. If the share price goes up, then the % return is much greater with options than with the underlying.

Analysing Options

Writing call options is extremely risky as the potential for losses are unlimited. This changes when the writer own the shares on which the call is written (a covered call in relation to a naked call). Page 15 of the book includes a few nice pay-off diagrams that are normally used when looking at option returns. If you start looking at these charts you can imagine that almost everything is possible with mixing different kinds of options. When looking at a portfolio of options, the best way to draw a pay-off diagram is by first using a table with values for the different options at different share prices, allowing your to find the sum of their values and to draw the pay-off diagram.

When writing a covered call, the only downside is loosing the share when the option is excercised, otherwise, there will be a profit because the share pay-off will run contra the option pay-off when the share price rises.

Call option prices decrease as exercise price increases and the other way arround. All this flexibility might allow for arbitrage, risk-free profits with options through differences in pricing on the same product. Due to liquid markets, any such situations are traded away swiftly.

There are several propositions in relation to options:

1\. Share Price >= Call Price >= max (0, Share — excercise price)

2\. Price of a call option increases as the time to expiry increases

3\. Price of call options decrease as they exercise price increases

4\. Value of American call options = value of European call option

5\. Put = Call — Share price + PV(exercise price)

Option valuation

1973 Fischer Black and Myron Scholes introduced a new model to value options and it only needed readily observable values. The Black-Scholes model has since retained its position as the most popular option valuation tool. Another method is the binominal method by Cox, Ross and Rubinstein (1979), which might be simpler to understand, is more flexible but is very difficult to compute. The Black-Scholes formula looks difficult but is easy to use within spreadsheets.

There are different variables in the formula that have an effect on option prices:

1\. Current Share Price — Excercise Price

2\. Volatility is good, as we just let it expire if it is down, but higher volatility makes it more likely to be high

3\. time to expiry means that when the time increases, the price increases too

4\. the risk-free interest rate, included for the time value, the higher this is, the higher the option value

The underlying idea is that you can always reproduce an option performance with a portfolio of the underlying shares and cash. The thing you can argue about though is number 2, being volatility, which is talking about the future until expiry, but is measured with a past value, something that can be different dependent on how you look at it. So you can also look at the market value at the moment and then work out the volatility that was used to calculate the market value by the market maker.

Currency options are frequently used in treasury management. Graman and Kohlhagen (1983) developed an adapted Black-Scholes for currency options. There is an important difference between options and forwards, because options are only the right to do something but forwards are a contract, meaning that you will have to e.g. exchange money at the time the contract states. Options are good because they limit downside risk, without taking away upside potential and can be used when you are not even shure if a cash flow will occur. Sometimes they also do not require daily margins as the forward market does. The rise of OTC currency options gave rise to a market for traded options.

Risk and Policy

This is more about a financial risk management rather than general risk, but again, risk mapping can be helpful. In general, the methods used need to fit the market and business as well as the size of a company. Not everybody needs or can finance a treasury function for example. You should actually take a look at the entire organisation and beyond financial risks.