The Monte Carlo pricing method is a flexible and powerful technique. Within a basic Monte Carlo pricing framework a simulation is set up that produces random realized option payoffs. The simulation is then run many times and the resultant payoffs are averaged to obtain option valuations.

For each currency pair within the simulation the following market data is required:

- Spot (
*S*): the current exchange rate in a given currency pair - Interest rates (
*rCCY1*and*rCCY2*): continuously compounded risk-free interest rates in CCY1 and CCY2 of the currency pair - Volatility (
*σ*): the volatility of the spot log returns

We start in Black-Scholes world so only a single volatility (no term structure or smile) and single interest rates (no term structure) are specified at this stage.

The simulation contains multiple time steps so the time (measured in years) between steps must be defined. For daily time steps, weekends can be removed and it is usually assumed that there are 252 trading days in the year; hence the time step is . As a sense check, at the 252nd step, time should be exactly 1:

The following formula is used for calculating the spot evolution between time steps within the simulation:

where is generated ...

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