Unspanned Stochastic Volatility, Conformal Symmetries, and Stochastic Time

Abstract

For the last decade, short-term rates of major currencies were consistently low and occasionally negative. Meanwhile, longer-term rates remained relatively high and volatile. This phenomenon added extra complexity to the the already formidably difficult task of pricing and hedging interest rate derivatives, rendering conventional approaches virtually defunct. We have observed that the application of jump diffusion in conjunction with conformal geometry allows to successfully tackle such market behavior in a fully consistent, tractable, and computationally efficient manner. The approach provides explicit parametric yield curves with arbitrage-free dynamics, and, in certain cases, even closed-form formulae for yield distributions. This is achieved without compromising efficiency or calibration flexibility. In particular, the 4D version of the model has been successfully calibrated to the swaption market with acceptable precision. The methodology has been applied in valuation of various exotic interest rate derivatives.