# 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 :)

• Would it not be better to restate this problem in simpler terms first, i.e. have only 1 timestamp instead of 2. Perhaps use a swap instead of a xccy swap. Then answers can potentially be built upon to attain the level of complexity without necessarily starting out there?
– Attack68
Commented Mar 16 at 15:33
• I understand your reasoning, but if the problem is too simple, there is no point on sharing it with a broader community, as answers are already on Google. Commented Mar 16 at 15:40
• What have you tried so far? Or is this homework and you don't want to do it yourself? Commented Mar 16 at 22:53
• Assume I pay fixed and receive float. If I can chose, I will always want to lower my fixed payment as much as possible and increase my float payments. However, what would be the purpose of such a structure, if that's not just a thought experiment?
– user70573
Commented Mar 16 at 23:40