I was modelling the swaption volatility smile with SABR using the following steps: Using a pre-determined set of SABR parameters, I priced a set of swaptions across a range of strikes [0.020, 0.090], with an initial forward rate of 0.045. These pricings are done Monte Carlo style by letting the forward rate and volatility evolve stochastically. A strike that is <= 0.045 I price it as a put, else I price it as a call. Each implied volatility across its strike is deduced using Brent from their corresponding swaption prices. There is no discounting done in the Monte Carlo simulations i.e. discounting the average of the terminal payoffs. I noticed that the swaption volatility smile I produced exhibited greater "choppiness" on the right side as compared to the left side i.e. on the OTM call side as compared to the OTM put side. Question : Can anyone tell me if this is an expected feature of the swaption volatility smile? Additional information on parameters and varying experimentations - My SABR parameters are [F0, sigma0, alpha, beta, rho, T, K] = [0.045, 0.058, 0.60, 0.5, 0.00, 1, 0.045] where sigma0 is the initial volatility and alpha is the vol-of-vol to avoid confusion. (1) A normal vol smile with 252 steps per year with 10,000 paths per Monte Carlo simulation, (2) Increase the number of steps per year to 1000 from setup (1), and (3) Increase the number of paths per Monte Carlo simulation to 100,000 from setup (1). (1) Number of Steps Each Year = 252, Number of Paths in Monte Carlo Simulation per Option = 10,000 (2) Number of Steps Each Year = 1000, Number of Paths in Monte Carlo Simulation per Option = 10,000 (3) Number of Steps Each Year = 252, Number of Paths in Monte Carlo Simulation per Option = 100,000
Asymmetric Choppiness in Swaption Vol Smile with SABR Model
KaiSqDist

