Monte Carlo Pricing of Rolling Zero-Coupon Bonds Under Simulated Rates

Summary

The document describes an attempt to estimate monthly zero-coupon bond prices for a fixed maturity using simulated interest-rate paths. It expresses each bond price as the expected exponential of the negative accumulated short rate over the remaining maturity, then proposes generating rate paths with Euler discretization and averaging discounted values across simulations.

The example uses monthly time steps and a three-year maturity, but it does not include a response identifying the error. The key implementation issue to investigate is whether the discretized integral uses the correct time increment and whether each rolling valuation window ends at the intended maturity date. The text provides no model specification, numerical output, or validation, so it is a problem statement rather than a complete pricing procedure.

Key ideas

• A zero-coupon bond price under simulated short rates is estimated from discounted accumulated rates to maturity.
• Monte Carlo estimation averages discount factors across simulated interest-rate paths.
• For monthly valuations, each calculation must use the appropriate remaining-maturity window along the simulated path.
• The document does not supply a solution or validation of the proposed discretization.

Tags

# How to price zero coupon bonds with the Monte Carlo method?


# How to price zero coupon bonds with the Monte Carlo method?












Im trying to calculate monthly ZCB bond prices with a fixed maturity T, over a period of months via Monte Carlo methods.

Here is my attempt:

For the first month, the price is $P_{t_0}(0,T) = E[exp(-\int_{t_0}^T r_s ds)]$, for the second month, the price is $P_{t1}(0,T) = E[exp(-\int_{t1}^{T+t1} r_s ds)]$, and so on up to the last month.

I construct N interest rate paths $r_t$ via Euler discretization, and approximate the expectations by taking the mean of each row of the matrix with elements

```
exp[-(T/M+1)*sum(r_s[t_i:t_{i+M}, j])]
```

where M is the number of months between maturity T and the "start month" of the bond price, j from 1 to N.

The maturity T is 3 years. So I let dt = 1/12 (in the Euler discretization) and T=3.

Where does it all go wrong?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.