Learn how to price options with the Monte Carlo method, and get a pricing spreadsheet for European, Asian, Barrier and Lookback options. Several methods exist to price options. Binomial trees , for example, calculate the value of an asset over a series of time steps.

At every step, the asset price can increase or decrease based on an up or down probability. In the first step, we generate many future stock prices. The following equation, for example, describes how a stock price varies over time given a Weiner process.

Once the entire set of S T is generated, the payoff is calculated.

Given a European option, the expected present value of call c t and put p t options are calculated as follows, where X is the strike price. The exponential term in the above two equations discounts the price at time t to expiry at time T.

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Then given an entire set of c t or p t , the mean option price is calculated. For example, for a call option, the mean price is. This VBA function uses the principles described above to price a European option.

European vanilla option pricing with C++ via Monte Carlo methods | QuantStart

The Lookback option has a floating strike, and you can choose an arithmetic or geometric average for the Asian option. Download Excel Spreadsheet to Price European Options with Monte Carlo.

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