# Monte Carlo Forward Rate Simulation

The Monte Carlo simulation is an alternative method of modeling interest rates that works by generating a large number of potential interest rate paths to discover how the value of a security may be impacted over time. The paths are then calibrated to ensure arbitrage-free valuation. This holds when the average present value across all possible interest rate paths for each benchmark security is equal to the security market value.

Adding a drift parameter to all the interest rates ensures that the Monte Carlo model is arbitrage-free and fits the benchmark spot curve. This method is applicable where the security’s cashflows are path-dependent. An example is a mortgage-backed security (MBS).

The model may impose upper and lower bounds consistent with mean reversion rates. Mean reversion tends to move the interest rate from the benchmark yield curve toward the implied forward rates.

## Question

The Monte Carlo method is most likely used for valuation of:

1. Path-dependent securities.
2. Option-free bonds.
3. Bonds with embedded options.

#### Solution

The Monte Carlo method is applicable where the security’s cash flows are path-dependent. An example is asset-backed securities.

Reading 29: The Arbitrage-Free Valuation Framework

LOS 29 (h) Describe a Monte Carlo forward-rate simulation and its application.

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