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 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
Swaps 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, · fixed rate set · constant in the range of 7% to 9%, and · variable in the range of 7% to 8%.
Benchmark pricing was based on the initial term structure of forward rates. FP pricing was based on 10,000 Monte Carlo paths with · LIBOR rate volatility set · constant at 10%, 25% and 50%, and · upward rising, initially at 25%, with 10% increments at each reset date thereafter, and with · adjacent LIBOR rate correlation constant in the range of 95% to 99% inclusive. Benchmark and FP prices were found to be essentially identical.
Barrier options were specified based on the following parameters · short rate equal to three month LIBOR, · tenor equal to three years, · initial forward rate term structure linearly upward rising , initially at 7% , with .0025 increments every three months, · strike equal to 10%, · upper and lower barrier levels respectively equal to 10% and 5%, · LIBOR rate volatility set constant at 10% and 25%, · adjacent LIBOR rate correlation equal to 98% inclusive.
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