This project simulates the dynamics of the USD/INR exchange rate. The stochastic differential equation used for the simulation has been derived by the repository owner from the book "Brownian Motion Calculus", specifically problem 4.10.8.
The specifics of the equation are derived from the mentioned book. For a clear representation, it's advisable to refer to problem 4.10.8 of the book.
The simulation was carried out with the following parameters:
- Initial exchange rate: 1 USD = 83 INR
- Drift rate: 1% annual appreciation of USD against INR
- Volatility: 15% annual volatility
- Time horizon: 1 year
- Time step: 1/252 (assuming 252 trading days in a year)
The next-day forecasted average exchange rate is approximately INR 83.01 per USD, with a standard deviation of approximately INR 0.78.
The results are visually represented in the plot provided in this repository.
To run the simulation, execute the exchange_rate_simulation.py script.
The dynamics and methodology are based on:
- Wiersema, Ubbo F. Brownian Motion Calculus. Wiley, 2008.
MIT License.