Vanilla option monte-carlo demo

This demonstration illustrates the use of the Monte Carlo technique for pricing vanilla calls and puts.

There is also a barrier option demo.

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

• 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.
• 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 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.
• 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.
• Black Scholes price is the option price as calculated by the ubiquitous Black Scholes option pricing formula.
• Black Scholes delta is the proportion of the underlying asset that you would need to buy or sell to hedge the value of the option against movements in the asset price. (For example, if you were to buy $1,000 worth of Microsoft share calls, and the delta was 0.5, you would need to sell $500 worth of shares to hedge changes in the value of the option). This can also be thought of as the probability of the option being exercised.
• 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 the Black Scholes price. 1,000,000 iterations will give you a fairly accurate price, but it does take some time to run!