Modeling a Path-Dependent Cross-Currency Swap with Rate Choices

Summary

The document poses a pricing problem for a cross-currency swap whose fixed and floating rates can be adjusted at two future timestamps. Starting from an initial fixed rate in one currency and floating rate in another, it describes three possible rate settings at the first decision and nine resulting paths at the second. The holder is assumed to control which path is taken, making the contract dependent on sequential choices as well as on the rates along the selected path.

No valuation method, market inputs, or numerical evidence are supplied; the text is a question rather than a worked analysis. A model would need to specify how the rate choices affect cash flows and whether the decision maker maximizes or minimizes value, along with discounting, currency conversion, and any exercise or transaction constraints. The example therefore frames a problem in path-dependent valuation but does not resolve how to price it.

Key ideas

• The swap has a fixed-rate leg in one currency and a floating-rate leg in another.
• The contract allows both rates to be adjusted at two decision times.
• Three intermediate settings create nine possible final rate paths.
• Pricing depends on who controls the path and how choices affect future cash flows.
• The document raises the modeling question but provides no proposed valuation method.

Tags

# Price Path Dependent Swap


# Price Path Dependent Swap












Let's say we start at t0, with a vanilla XCCY Swap contract (one leg paying Fixed Rate r, and denominated on Ccy1, the other leg paying Floating Rate f on Ccy2).

Now let's assume you have two timestamps at which you can decide to increase\decrease, or keep both fixed\floating rates constant. This simply means we have a tree with 9 final paths, one example would be something like,

- t0 -> Fixed Rate = r; Floating Rate = f

- t1 -> Fixed Rate = r; Floating Rate = f1

- t1 -> Fixed Rate = r - 5bps; Floating Rate = f1 - 3bps

- t1 -> Fixed Rate = r + 5bps; Floating Rate = f1 + 3bps

- t2 -> Fixed Rate = r + 10bps; Floating Rate = f2 + 6bps

- t2 -> Fixed Rate = r + 5bps; Floating Rate = f2 + 3bps

- t2 -> Fixed Rate = r ; Floating Rate = f2

- t2 -> Fixed Rate = r + 5bps; Floating Rate = f2 + 3bps

- t2 -> Fixed Rate = r ; Floating Rate = f2

- t2 -> Fixed Rate = r - 5bps; Floating Rate = f2 - 3bps

- t2 -> Fixed Rate = r ; Floating Rate = f2

- t2 -> Fixed Rate = r - 5bps; Floating Rate = f2 - 3bps

- t2 -> Fixed Rate = r - 10bps; Floating Rate = f2 - 6bps

Those would be the 3 intermediate possible paths (t1), and final 9 paths (t2). How would you price\model this product, assuming you have full control over the path you want to take, at each timestamp (t1, and t2)?

Hope you find this an interesting problem\question :)

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