> For the complete documentation index, see [llms.txt](https://finwhite.gitbook.io/variableswap/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://finwhite.gitbook.io/variableswap/variable-rate-swap-valuation.md). # Variable Rate Swap Valuation Variable Rate Swap Analytics Variable rate swap is a special type of interest rate swap in which one leg of the swap corresponds to fixed rate payments while the other involves fixed rate payments for an initial period of time and a floating rate for the rest. The floating rate on that portion is defined as a minimum of two index rates. The fixed rate leg is similar to a fixed rate bond. The bond price is computed by discounting each coupon descripted at We treat the two index rates as assets whose values are lognormally distributed random variable. Their pricing procedure uses discount factors retrieved from the EURIBOR curve. The present value of the minimum of two assets, *s1* and *s2*, is given by the formula (1) where · , · s1 and s2 are the volatilities of *s1* and *s2* respectively, · r is the correlation of the two risk factors, · *T* is the maturity time, · and are the expected values of *s1* and *s2* at maturity (future values), · *D(T)* is the discount factor implied by the yield curve. It is forward two index rates as retrieved from the yield curves that should be used for and . The minimum of two values, *s1* and *s2*, can be expressed as *p = min(s1,s2) = s1 – max(s1-s2, 0)* (2) If *s1* and *s2* are two risky assets, the present value of *p* at some future time *T* is (3) where *P(0,T)* is the discount factor implied by the yield curve. Assuming the asset values lognormally distributed, the expectation of *max(s1-s2, 0)* at maturity can be found as the value of the so called “Exchange-One-Asset-for-Another” European option (see ) and is given by the following equation: (4) where · · s1 and s2 are the volatilities of *s1* and *s2* respectively, · r is the correlation of the two risk factors · *T* is the maturity time · and are the expected values of *s1* and *s2* at maturity (future values). Combined, Eqs. (2), (3) and (4) yield (5) --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter: ``` GET https://finwhite.gitbook.io/variableswap/variable-rate-swap-valuation.md?ask=&goal= ``` `ask` is the immediate question: it should be specific, self-contained, and written in natural language. `goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.