- What will it run on, and how do I install it?
- Why doesn't the tool fit my screen?
- How do I check monitor resolution?
- Which option pricing model should I use?
- How does the tool handle the possibility of early exercise?
- Why does the strategy evaluation tool include Black-Scholes if the binomial tool handles all situations?
- How can I use the tool for options on stock indices, currencies and futures?
- How can I identify optimal early exercise points?
- When is it optimal for an option to be exercised?
- Will an early exercise decision always turn out to be correct?

### What will it run on, and how do I install it?

A fairly fast processor (>200MHz) is recommended. The tool will run on Windows 95/98, Windows NT or Windows 2000. Microsoft Excel 97 or above is required.

Please read the disclaimer before you download the program. Downloading the Strategy Modelling Tool indicates your acceptance of the terms of the disclaimer.

Download the Strategy Modelling Tool.

### Why doesn't the tool fit my screen?

The strategy modelling tool defaults to a size to suit screens of 1024 x 768 resolution. However, it can be changed to suit lower resolutions. To find out how to change the settings, or to determine and change your monitor resolution, read below.

### How do I check monitor resolution?

- Windows: to adjust monitor resolution, right mouse click on the PC desktop. Select “Properties”, choose “Settings” and slide the scale as required.
- Mac: using the main menu go to “Control Panel”. Select “Monitors” and choose an appropriate setting from the list. If 1024 x 768 is not available then select the highest setting.

### Which option pricing model should I use?

The tool lets you choose the way options are priced. You can choose from the following models:

- Back-Scholes - European
- binomial - American
- binomial - European

Most exchange traded equity options on ASX are American options, meaning that they can be exercised before the expiration date.

If the options are European exercise, meaning they can only be exercised on their expiration date, then you can select either Black-Scholes or the Binomial European.

Unlike the binomial model which can price both American and European options, the Black Scholes model can only be used to price European options accurately, although for non-dividend paying stocks the American call price is the same as the European call price and all three formulas produce the same result. This is because, assuming no arbitrage opportunities (i.e. the call is fairly priced) and ignoring transaction costs, there is never any (rational) reason to exercise a call option over a non-dividend paying stock early.

### How does the tool handle the possibility of early exercise?

For call options on dividend paying stocks there may be times, just prior to ex-dividend dates, when it is worthwhile to exercise the call before expiration. Also prior to ex-dividend dates, European calls may be worth less than their intrinsic value - this cannot happen for American calls. So for dividend paying stocks the American call may be worth more than the European call - it has an early exercise premium, the size of which varies according to the time to ex-dividend date and other factors. The binomial American model is able to handle this situation; the Black-Scholes model, however, cannot as it only takes into account the position at expiration.

The situation is different for put options. Even on non-dividend paying stocks, the fair value of a deeply in the money European put can be less than its intrinsic value (due to the carrying costs of the positions which arbitrageurs undertaking conversions would have to carry through to expiration). American puts, on the other hand, cannot trade at a discount to parity as they would quickly be exercised by arbitrageurs.

It may also be optimal to exercise a deeply in the money put early. An example would be if the stock price fell to zero because the company went bankrupt. In this case there would be nothing to gain (and in fact something to lose) by waiting until expiration. Other less extreme cases could also justify early exercise.

Because it may be worthwhile to exercise an American put early, American puts will always be worth more than European puts.

To identify optimal early exercise thresholds for American options you can use the tool’s early exercise report.

### Why does the strategy evaluation tool include Black-Scholes if the binomial tool handles all situations?

Including the Black-Scholes model lets you compare results with those provided by the binomial tool. However, even if you don't explicitly choose to use the Black-Scholes method of pricing it is still used extensively by the tool for producing time-lines on the pay-off diagrams, as it is much faster than the binomial tool. This is because Black-Scholes is an analytical formula, which produces an accurate result in a couple of lines of code, whereas the binomial method is a numerical tool based on iterating through a large number of steps.

For more information on the approach to pricing see the section on Option Pricing Models.

### How can I use the tool for options on stock indices, currencies and futures?

These options are handled by the tool as follows:

Options on foreign currencies: Set the continuous dividend yield for the currency option (just as you would for an equity option) equal to the foreign risk-free rate. This is because holding foreign currency, which will pay you interest at the foreign risk free rate, is analogous to holding stock paying a continuous dividend. Options on both these underlying assets are handled in the same way.

Options on stock indices: Set the continuous dividend yield for the index option equal to the average dividend yield on the stocks in the index.

Options on futures: Set the continuous dividend yield for the option on the futures contract equal to the risk-free rate.

Then select European or American pricing in the normal way.

### How can I identify optimal early exercise points?

This tool highlights those price/time combinations where it would make financial sense to exercise early. To identify optimal early exercise points go to the 'Early Exercise' worksheet and run the report.

This will identify the theoretical optimal early exercise thresholds - the underlying asset price/date combinations where it may be optimal to exercise the option - for the range of underlying assets being evaluated on the strategy evaluation worksheet. All options (which must be American-style exercise) will be searched for optimal early exercise points.

This information is useful to both option holders and option writers. If you are a holder and either exercise too early or continue to hold beyond the optimal exercise date then you are not maximising your profit potential; if you are an options writer then you need to be able to anticipate the risk of early exercise so you can take evasive action in advance of this happening

Note that American options can be exercised at any time prior to maturity - an option holder is not obliged to act rationally, and thus financially unsound early exercise 'decisions' are sometimes made.

### When is it optimal for an option to be exercised?

The early exercise threshold produced by the tool using the rules below is the theoretical optimal price/time combination for early exercise. Note that in practice bid/ask spreads, transaction costs, taxes and other market conditions can change this threshold significantly.

The following is a brief summary of the rules followed by the tool in producing early exercise thresholds:

Call option - no dividends - never.

Call option - discrete dividends - on the day before the ex-dividend date(s), providing the dividend is greater than the present value of the cost of holding the underlying asset to expiration, and the time value premium remaining on the call is negligible (i.e. the call is well into the money).

In practice, when there are multiple dividend payments the optimal exercise time will usually (but not always) be the day before the last ex-dividend date. Note that it is never theoretically optimal to exercise a call just to collect the dividend as the price of the underlying asset can be expected to fall by the amount of the dividend on the ex-dividend date. You would only exercise a call and carry the underlying asset as an alternative to holding the option, not simply as a way of collecting the dividend.

Call option - continuous dividends - when the present value of the dividend stream on the underlying stock is greater than the present value of the cost of holding the underlying asset to expiration and the time value premium remaining is negligible (the tool lets you adjust the sensitivity of 'negligible'.)

Put option - when the put is sufficiently in the money so that time value premium remaining is negligible (the tool lets you adjust the sensitivity of 'negligible'.)

The lower the risk free interest rate the deeper in the money and the closer to expiration the put will have to be to reach the early exercise threshold. If there is a discrete dividend and it is greater than the present value of the cost of holding the stock to the ex-dividend date then it is not usually optimal to exercise the option before the ex-dividend date. It is often optimal to exercise a put exactly on the ex-dividend date.

### Will an early exercise decision always turn out to be correct?

No. If, after exercise and on or before the option maturity date the underlying asset price moves so that the option, had you held it, would be out of the money, then you could be worse off having exercised early.

As the option taker, you have the choice of selling or exercising your option. Theoretically it is always better financially for an option holder to sell the option in the secondary market (and then to buy or sell the underlying asset at market price if required) rather than exercising, when there is time value premium remaining on the option.