IR Vol
FinPricing offers:
Four user interfaces:
- Data API.
- Excel Add-ins.
- Model Analytic API.
- GUI APP.
Implied Volatility
| 1. Introduction |
An implied volatility is the volatility implied by the market price of an option based on an option pricing model. A volatility surface is derived from quoted volatilities that provides a way to interpolate an implied volatility at any strike and maturity.
There are two types of interest rate implied volatilities: cap implied volatility and swaption implied volatility. An interest rate cap implied volatility surface is a three dimensional plot of the cap implied volatility as a function of strike and expiry, while an interest rate swaption implied volatility surface/cube is a four dimensional plot of the swaption implied volatility as a function of strike and expiry and tenor. Bermudan swaption impliend volatility surface is similar to swaption implied volatility surface but calibrated via Bermudan swaption quotes.
The term structures of implied volatilities provide indications of the market’s near- and long-term
uncertainty about future short- and long-term swap rates. A crucial property of the implied
volatility surface is the absence of arbitrage.
When the implied volatilities are plotted against the strike price at a fixed maturity, one often observes a skew
or smile pattern, which has been shown to be directly related to the conditional non-normality of the underlying
return risk-neutral distribution. In particular, a smile reflects fat tails in the return distribution whereas a skew
indicates return distribution asymmetry. Furthermore, how the implied volatility smile varies across
option maturity
and calendar time reveals how the conditional return distribution non-normality varies across different conditioning
horizons and over different time periods.
The pricing accuracy and pricing performance of option valuation models crucially depends on
absence of arbitrage in the implied volatility surface: an input implied volatility surface that is not arbitrage-free
invariably results in negative transition probabilities and/ or negative volatilities, and ultimately, into
mispricings.
Traditionally, interest rate was always positive and hence the Black-Scholes was based on lognormal assumption. Consquently interest rate implied volatility is quoted via absolute strikes.
After finanacial crises, the majority of bonds in Europe and Japan carry negative yields to maturity, i.e., negative interest rate. Under this scenario, savers are punished but borrowers get rewarded for borrowing money. Negative interest rates are unlikely to change in the coming years. Consequently option pricing model evolves from lognormal assumption to normal assumption that requires relative strike. The relative strike is defined as forward rate - ATM rate.
FinPricing uses the SABR model to construct swaption implied volatility surfaces. The constructed volatility surface is very finely granular so that users can directly uses linear interpolation to calculate in-between values without arbitrage. The newly-generated surfaces look like
You can find interest rate volatility calibration and construction at Swaption Implied Volatility Construction.
| 2. Related Topics |