Swap Pricing Discussion

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在這裏可以討論一下如何為某些產品作出定價嗎？

我知道普通的Interest Rate Swap可以用bootstrapping的方法從yield curve計算出不同的discount factor然後再得出swap的價格, 但這種方法是指floating rate於該期作出fixing之後, 下一期才派息.

如果我的floating rate leg派息是以期間floating rate的平均值計算, 那我是否仍可以bootstrapping方法計算出來？用SIMULATION似乎太複雜, 也需要用上HJM / BGM 模型.

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关键词：Discussion Pricing discuss Pricin DISC discount factor 平均值 模型 如何

你这个是asian-style interest rate swap,需要一个利率模型，如果不想用HJM/BGM,10年前有台湾人搞过Vasicek
还有，plain vanilla interest rate swap,也不是从yield curve定价的，yield curve和discount factor本来就是从swap curve bootstrap出来的

irvingy 发表于 2012-2-12 21:51
你这个是asian-style interest rate swap,需要一个利率模型，如果不想用HJM/BGM,10年前有台湾人搞过Vasicek ...

當然yield curve可以由swap組成, 但中短檔期可以由其他產品組成. 其實有關interest rate swap的平均值, 好像很少有書提及, 我也不知道怎樣計算expected future rate....

Could you explain in more detail like what index is used for floating leg?

Consider a Q/Q swap. Is the floating leg reset on 3M Libor average? Or daily average like OIS? Rolling or simple average?

OK. Take an example.

arithmetic average of Libor 3M vs 3%, quarterly pay, quarterly reset in advance. It is not normal swap in the market, but I just simplify it.

Sorry never handled this kind of product, but below are some of my thoughts.

Let's further simplify it as a floating loan maturity in 90D, paying arithmetic average of Libor 3M at the end (i guess averaging payment can only be reset arrears, at least the first payment?)

To hedge against it, I can enter in 90 forwards:

1) start at t0 + 0, indexed to Libor 3M, matured t0 + 90
2) start at t0 + 1, indexed to Libor 3M, matured t0 + 90
...
90) start at t0 + 89, indexed to Libor 3M, matured t0 + 90

For each of above, the Libor 3M rate can be estimated via implied forward curve, isn't it?

Revision of above:
Interest payment at the end = sum_t [ forward(t, t+90) ] / 90 * (90/365)

You can get each forward(t, t+90) from the implied forward curve?


BTW, they are just all textbook models, nothing works under single curve framework nowsday.

oddsmaker 发表于 2012-2-13 22:26
Revision of above:
Interest payment at the end = sum_t [ forward(t, t+90) ] / 90 * (90/365)

I have similar idea with you. btw, nowadays the market becomes multiple curves pricing already. I don't know if China is using single curve still.

I am now thinking if any adjustment is needed on the rates.

I suppose at least two curves is needed for your case.

A forward estimation curve with all underlying instrument paying quarterly (e.g., no semi- instrument).
A discount curve, maybe OIS?

It depends on your counterparty and collateral you used if CSA is done.