Monte Carlo Multi-factor Short Rate Model
The Monte Carlo Multi-factor Short Rate Mode has been used extensively in pricing a variety of interest rate derivative securities. The model assumes that short rates at reset times are lognormally distributed.
Caplets were specified based on the following parameters :
· short rate equal to three month LIBOR, · tenor equal to three months, one year and three years, · initial forward rate term structure set · constant at 7%, 7.5% and 8%, and · linearly upward rising , initially at 7% , with .0025 increments every three months, · strike equal to 7%, 8% and 9%, · LIBOR rate volatility set constant at 10%, 25% and 50%, and · adjacent LIBOR rate correlation constant in the range of 90% to 99% inclusive.
Caplets were benchmarked using Black’s model, that is, with constant volatility and with fixed discounting based on the initial term structure of forward rates; FP prices were based on 10,000 Monte Carlo paths. Numerical test results showed relative differences between the benchmark and FP model
· not greater than 1% for high (50%) volatility, · not greater than .1% for low (10%) and medium (25%)volatility.
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