從對數正態波動率報價中獲取掉期期權價格

I am working with the following dataset from quandl: https://www.quandl.com/databases/CSWO (I’m using the sample dataset only). My question is how to obtain the swaption prices from the quotes given. The dataset gives me the following information for each contract:

1. Currency (in the sample data set only Australian dollars).
2. Option tenor. I will denote it with [Math Processing Error] $ T_{\text{option}} $ .
3. Swap tenor. I will denote it with [Math Processing Error] $ T_{\text{swap}} $ .
4. How much the option is in/out of the money given in basis points, e.g. P100 means that the strike is 100 basis points above the ATM strike (Is the ATM strike equal to the current forward rate [Math Processing Error] $ F(t; T_{\text{option}}, T_{\text{option}}+T_{\text{swap}})) $ for the time interval [Math Processing Error] $ [T_{\text{option}}, T_{\text{option}}+T_{\text{swap}}] $ ?)

My approach to obtain the swaption prices would be the following: lognormal vola quotes means the Black swaption formula was used to compute the implied volatility. The formula is (see for example page 19 in https://courses.maths.ox.ac.uk/node/view_material/3748):

[Math Processing Error]$$ V^{\text{payer swaption}}(t) = A(t)\left\lbrack R^(t)N(d_1)-RN(d_2)\right\rbrack $$ where [Math Processing Error]$$ d_1 = \frac{\log\left(\frac{R^(t)}{R}\right)+\frac{1}{2}\sigma^2(T_0-t)}{\sigma (T_0-t)}, \quad d_2 = d_1 -\sigma\sqrt{T_0-t} $$ and $$ A(t) = \sum_{i=1}^n\delta_kP(t,T_k) $$ 與付款日期[數學處理錯誤]和 $ T_k $ $ \delta_k = T_k-T_{k-1} $ （數據集文件中沒有提及付款頻率。我怎麼知道使用的頻率？）。[數學處理錯誤]是可以行使交換權的時間。[數學處理錯誤]是交換的罷工和 $ T_0 $ $ R $ $ R^*(t) $ 是該時間段的遠期匯率 $ [T_0,T] $ 在哪裡 $ T=T_n $ 是互換到期的時間。現在的問題是如何在上述公式中插入給定的數據。我會這樣做：

1. 為了 $ R^*(t) $ 選擇從掉期開始的掉期利率[數學處理錯誤] $ T_{\text{option}} $ 並成熟於 $ T_{\text{option}}+T_{\text{swap}} $ .
2. 放 $ R=R^*(t)\pm \text{basis points offset of ATM strike} $ .
3. 為了 $ \sigma $ 選擇引用的隱含波動率。
4. 計算 $ A(t) $ 首先必須引導一條零曲線並獲得 $ A(t) $ 從那個零曲線。我用什麼工具來引導零曲線，我該怎麼做？

Are your implied vols definitely log-normal? Is there any lognormal shifting applied? If not you will struggle to compute the log of say (0.3%/-0.7%) for a swaption which is P-100 in currencies such as EUR and JPY and to some extent GBP and USD.

Swaption prices are often quite useful without the discounting element.

For example consider two prices;

5y30y: with 50bps normal vol or, say, 40 logvol might be priced at 35bps. 
Factoring the PV01 of a 1mm 5y30y swap of, say, 2300 gives a cash value of 80,500 (2300 x 35).
This is a cash price of 805bps of notional.

vs

5y5y: with 50bps normal vol or, say, 40 logvol might be priced at 35bps.
Factoring the PV01 of 1mm notional, say, 450 gives a cash value of 15,750.
This is a cash price of 157.5bps of notional.

So monitoring the above it is actually more difficult to standardise and evaluate the swaptions whose cash price is stated rather than rate price, which in this case is the same at 35bps.

這取決於您希望計算貼現曲線的精確程度，但一個非常粗略的衡量標準是獲取 1Y、2Y 3Y 等的掉期價格，然後使用wiki IRS 定價中的公式來確定您可以使用的貼現因子點插值，對數線性或對數三次：

$$ R = \frac{x_0-x_{n_2}}{\sum_{i=1}^{n_1} d_i x_i} $$

引用自：https://quant.stackexchange.com/questions/39123