Barrier option monte-carlo demo

This demonstration illustrates the use of the Monte Carlo technique for pricing pricing barrier calls and puts. Barrier options are also known as 'knock in' and 'knock out' options.

There is also a demo for vanilla options.

The barrier options priced here come in two flavours, 'knock ins' and 'knock outs'. A knock in option comes into being only when the spot price reaches the barrier prior to option expiry. The barrier may be above the initial spot price (and up and in) or below it (down and in). A knock out ceases to exist if the spot price reaches the barrier prior to expiry.

Some notes on the numbers that you input to the program:

• In/Out indicates whether this is a knock in or knock out.
• Spot is the current price of the asset. This may be, for example, 25.50 for a share or .5410 for the AUD/USD price.
• Strike is the price at which you will have the option to buy (call) or sell (put) the asset.
• Barrier price is the level the spot price must reach before the option is knocked in or out.
• Volatility is the measure of riskiness of the asset in terms of standard deviation. This is entered in percentage points. So 10% vol would be entered as '10'.
• Carry rate is the 'interest rate' that the asset pays. For a stock, this would be the estimated dividend yield. For a foreign exchange option, it is the interest rate of the 'commodity' currency, or the AUD interest rate in our AUD/USD example.
• Interest rate is the rate of the currency that the asset is priced in. In our AUD/USD example, it would he the USD rate. For an Australian stock, it would be the AUD interest rate.
• Years is the number of years from today to the expiry of the option. So for a six month option you would enters 0.5 years.
• Steps is the number of discrete steps each simulation path will take. Refer to the notes on the Monte Carlo process for details.
• Iterations is the number of simulation paths used for the Monte Carlo simulation.

Calculated information:

• The graph on the left maps each simulation path. The line is grey if the option is not yet knocked in, blue if knocked in and red if knocked out.
• The graph on the right shows the number of occurrences that the simulation paths end on a given final price. All being well, this should be in the shape of a normal distribution. The light grey bars count those paths where the option fails to knock in, dark grey shows the paths where the option knocks in but is not exercised, blue where the option is knocked in and exercised and red where the option is knocked out.
• Forward price is simply the current 'fair value' forward price for the asset at option expiry given the current price (spot) and the two interest rates.
• Merton's price is the option price as calculated by Merton's barrier option pricing formula.
• Monte Carlo price is the price as calculated by the simulation. You'll note that this changes each time the simulation is run. You should also see that the more iterations you specify, the closer the Monte Carlo price is to Merton's price. 1,000,000 iterations will give you a fairly accurate price, but it does take some time to run!