Callable Multi Range Accrual!
These are part of the rates exotic books at investment banks specially in the APAC region. I’ll give an overview of this trade and a broader idea of its pricing. In future posts I’ll give a detailed analysis of each of the pricing steps involved. Explaining each step in the pricing of this trade should effectively cover all aspects of rates exotic pricing in general.
First, what are rates exotics?
So you have interest rate swaps where 'fixed' cash flows are exchanged with variable ones periodically linked to some rate index (used to be Libor now it's mostly an RFR index like SOFR). If these can be cancelled or exercised around cashflow dates before the swap's maturity then you have what is called a callable swap or a Bermudan (Berm for short). Now coming to the 'fixed' component, investors might want a higher 'fixed' rate than what a swap available in the market currently is paying. To enhance the fixed rate investors might be fine to take exposure to a rates spread (steepener/flattener as they're called) or an FX in which case the ‘higher‘ fix they receive will be dependant on how those spreads or FX behave i.e. an optionality to these ‘indices’ is created. This makes the fixed coupon leg an exotic coupon leg.
Callable Multi Range accrual is one such trade and a pretty complex one at that. It can have two or more range accrual indices. Below is an example of a trade with 3 indices.
Example: Callable(cancellable) interest rate swap, over 10yrs maturity, exchanging the following exotic coupons yearly for quarterly funding coupons.
Exotic coupon: a fixed interest rate of say 4% accruing daily if the following conditions are met:
USD30Y minus USD5Y is positive
USD10Y CMS is below 5%
EURUSD is between 1 and 1.3
Pricing:
Pricing of this involves the following steps:
Price the non-callable/underlying coupons of this range accrual. This involves pricing daily digitals. With 3 indices this would mean computing tri-variate probabilities with correlations between the 3 indices also needed as inputs.
Calibrate a cross-currency tree model (as there are 2 currencies here) to USD & EUR swaption vols and EURUSD FX options taking necessary correlations as inputs. This step is modelling heavy!
Adjust the above tree so as to match non-callable coupons values arrived in step 1 (Adjusters come into play here)
Finally, price the callable over the adjusted tree through backward induction (start from end and proceed backwards solving expectations via numerical integration along the way). For 3 or more indices this is done using Longstaff-Schwartz (american monte-carlo) regression approach.
While the above are broadly the 4 steps, there are so many internal components i.e. pricers or solvers that the pricing of this exotic goes through.
I’ll cover each step in future posts.