I have broker data and I see three sets of swaption vol data:
- Lognormal (Black)
- Shifted Lognormal (Black with displaced diffusion)
- Normal (Bachelier)
The quotes are given by the following key (Date, Currency, Option expiry, Swap tenor, and Moneyness).
Moneyness is given on a fixed scale relative to the at-the-money forward in basis points from 12.5 to 300 ONLY - no data provided specifically for negative moneyness.
I am given quotes for:
- ATM vol
- Payer vol spread
- Receiver vol spread
- Payer premium (Forward and discounted)
- Receiver premium (Forward and discounted)
- Collar premium (Forward and discounted)
- Strangle premium (Forward and discounted)
My question is, how can I extract the implied volatilities for the negative moneyness? I.e. for basis points from -12.5 to -300. Please answer in the context of validating my assumptions defined below
Assumptions
I think the receiver swaption quoted is the negative moneyness payer as it gives a nice smile shape, but I am not an expert. (assumption 1)
I believe there may be some tricks to translate between the vols or prices that I am not aware of. Any input on using strangle/collar vols to correctly back out negative moneyness. (assumption 2)
Goal:
My ultimate goal is to (a) figure out the negative money implied vols via validating assumption 1, then to (b) see how to get a price from either normal or shifted lognormal model for negative moneyness by validating assumption 2.