Bermudan swaption pricing

Bermudan swaption pricing

Step 1. Import European Swaption ATM volatility matrix;

Step 2. Specify Bermudan Swaption details;

Step 3. Calculate Bermudan swaption price;

Case Study. Multi-callable swap;

Step 1. Import European Swaption ATM volatility matrix

• Press button Add... > Import Excel file
• Choose Excel file where volatilities are inserted (Browse...)
  • NB! For importing volatilities one can use template:   Add... > Import Excel file > European swaption ATM volatilities
  • NB! Excel file tab name must start with the prefix “vola”
• Press Import. Volatilities are imported into sals.a

Step 2a. Specify swaption details

Insert swaption choosing Add... > Manual Entry > Swaption (beta)

• Value date is the start date of underlying swap
• First Option Date is the first option maturity date
• Option Maturity Date is the last option maturity date
• Maturity is the last payment (end) date of underlying swap
  

Step 2b. Specify swaption details

• Strike is the option exercise rate;
• Exercise Type is the chosen Bermudan (multiple exercise dates)/European (one exercise date)
• Option Frequency is the frequency with which the option can be exercised (irrelevant for European type)
• Volatility is the European type swaption volatility (irrelevant for Bermudan type)
• Execute option is chosen Always
  

Step 2c. Specify swap details

• Underlying swap details can be specified in tab “Deal details”
  • For example: Payment Frequency > Quarterly
• More complex details (amortizing swaps, day count conventions etc.) can be specified in tab “Amortization” and “Expert Settings”.

Step 3. Calculate Bermudan swaption price

In the sals.a main view:

• Mark the Checkbox for the swaption deal:
  
• Press Report -> Report Options -> Bermudan Swaption Report (beta)

Result 1: Bermudan swaption price and excercise probabilities of option dates

Result 2: European swaption volatility matrix (ATM)

Case Study 1. Make swap multi-callable

The client wants to reduce current swap interest payments by selling the opportunity for bank to cancel the swap

• How much premium does this opportunity generate?

Callable payer swap

• Underlying swap
  • Type: payer swap
  • Length: 10 years (25.10.2007-25.10.2017)
  • quarterly payments
  • first nominal 25 367 381, semi-annually amortizing
  • swap rate 3.615%
• Bermudan swaption
  • Sell option
  • Type: payer swaption
  • maturity dates semi-annually
  • strike 3.615%
    

Multi-callable payer swap (underlying payer swap)

• Specify swap details as usual
• Swap price is seen in tab General Data > NPV

Multi-callable payer swap (Bermudan swaption)

1. Current swap start date
2. First possible exercise date
3. Last possible exercise date
4. Current swap end date
5. Buy/sell deal
6. Strike for option
7. Contract type (European or Bermudan)
8. Cancel frequency (NB! Has to be less frequent than underlying swap payment frequency)
   

NB! This is only swaption price. To get multi-callable swap price one has to add it to the underlying swap NPV

Callable swap price =
underlying swap
+
sell Bermudan swaption

In this case
- 621 729.49 (swap)
- 886 325.39 (swaption) =
- 1 508 054.88 (callable swap).

Case Study 2. Make swap multi-callable

Callable payer swap

• Underlying swap
  • Type: payer swap
  • Length: 5.5 years (30.06.2009-31.12.2014)
  • Semi-annually payments
  • first nominal 4 168 619, semi-annually amortizing
  • swap rate 4.6%
• Bermudan swaption
  • Sell option
  • Type: payer swaption
  • maturity dates semi-annually
  • strike 4.6%
    

Multi-callable payer swap (underlying payer swap)

• Specify swap details as usual
• Swap price is seen tab General Data > NPV

Multi-callable payer swap (Bermudan swaption)

1. Current swap start date
2. First possible exercise date
3. Last possible exercise date
4. Current swap end date
5. Buy/sell deal
6. Strike for option
7. Contract type (European or Bermudan)
8. Cancel frequency (NB! Have to be less frequent than underlying swap payment frequency)
   
   

NB! This is only swaption price. To get multi-callable swap price one has to add it to the underlying swap NPV:

-319 668.29 (swap)
-30 045.84 (swaption) =
-349 714.13 (callable swap).