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
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)
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.