Historically implied swaption skews using non-parametric methods - Jackson, Evan (Division of Actuarial Science, 2017)
This dissertation aims to derive historically realised volatilities for swaptions of a long-term nature within the South African market, which is illiquid and over-the- counter. To achieve this the dissertation adopts and constructs non-parametric methods which only make use of historical realised data of the underlying variable rather than any implied pricing history of the derivative itself. Stutzer's method of canonical valuation (1996) is adapted for use with interest rate derivatives of a long-term nature. However, under a simulation of swaption prices, canonical valuation is found to have a monotonic increase in pricing error for swaptions of maturities over 2 to 15 years. A new method is constructed, named the relative entropy approach, which is based on the work of Buchen and Kelly (1996) and is capable of pricing long-term interest rate derivatives using a smoothed continuous distribution of the historical realised data of the underlying variable only, while market implied pricing data can also be incorporated for calibration of the derivative to current market prices. Under simulation this method maintains consistent and bounded pricing error across swaption maturities of up to 15 years. This method is then used to obtain historical realised volatilities for swaptions of a long-term nature. The derived ten-year tenor swaption skews under the relative entropy approach observe smile characterisitcs similar to that of the market implied skew over short-term maturities and maintain a volatility smile, albeit diminishing, across moneyness for maturities up to 20 years. The skews are further tested for sensitivity to the input historical data as well as the precision of the skew under implementation of the relative entropy approach. Results show the derived swaption skews to be robust when using a historical data set greater than 1200 observations. The swaption skew is sensitive to the nature of the historical data used which is representative of particular market characteristics over certain historical periods. The relative entropy approach is concluded capable of pricing long-term swaptions in a market where little or no option pricing data exists and could be considered for use in practical applications.