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Pricing a Two-Year Interest Rate Swap with a Binomial Rate Tree

Article Quant Q&A · Author: David
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Summary

The document poses a swap-pricing problem in which the floating leg is represented by a risky rate that evolves on a two-period binomial tree. It supplies a risk-free rate and starting risky rate, along with upward and downward rate multipliers, and asks how to determine one fixed swap rate for a two-year interest rate swap. The central issue is how to combine the possible rate paths into a single fair rate.

The proposed approach is to enumerate potential paths and calculate path-specific swap rates, but the document does not provide an answer or specify probabilities, discounting conventions, or a valuation framework. Those details matter: a tree of possible outcomes alone does not determine a unique swap rate. The material therefore identifies the setup and an important pricing question, but is not a complete pricing method or worked numerical example.

Key ideas

  • A binomial tree can represent possible paths for a floating reference rate.
  • A swap’s fixed rate must be determined from the value of its floating and fixed legs.
  • Path-specific implied rates do not by themselves specify one fair swap rate.
  • Tree probabilities and discounting assumptions are needed for a complete valuation.

Tags

Fixed incomeDerivatives pricingStatistics
Full text
# How determine swap rate with binomial tree


# How determine swap rate with binomial tree












The risk free rate is $0,01$ while the risky rate follows a $2$ period binomial model and the risky rate at time $t=0$ is $1$, where $u= 1.5$ and $d=0.6$.

How can I determine a swap rate of IRS with maturity 2 years whose floating leg is represented by risky rates?

My idea is to create the binomial tree for the risky rate in order to have all potential paths. After that, I could recover 4 potential swap rates from these values but I have to determine only one swap rate.

How can I do that?

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