Hybrid smiles made fast

Risk management of equity-linked structured notes requires consistent modelling of both stocks’ smiles and stochastic interest rates. Existing approaches require costly computations to capture highly curved smiles – especially at long-dated maturities. Messaoud Chibane and Dikman Law show how a quadratic parameterisation of volatility, with some analytic approximations, can be much quicker

Since the late 1990s, equity-linked structured notes have become increasingly popular with retail investors, particularly in Japan. These products, such as enmansai and uridashi, provide some controlled exposure to stocks or indexes by embedding derivatives payouts with a floating rate in coupon payments. Given the dependence of option prices on forwards – and of the latter on rates – the interaction between the implied volatility smile of the underlying equities and the interest rate dynamics