Stochastic elasticity of variance with stochastic interest rates

This paper aims to improve the implied volatility fitting capacity of underlying asset price models by relaxing constant interest rate and constant elasticity of variance and embedding a scaled stochastic setting for option prices. Using multi-scale asymptotics based on averaging principle, we obtain an analytic solution formula of the approximate price for a European vanilla option. The combined structure of stochastic elasticity of variance and stochastic interest rates is compared to the structure of stochastic volatility and stochastic interest rates. The result shows that of the two, the former is more appropriate to fit market data than the latter in terms of convexity of implied volatility surface as time-to-maturity becomes shorter.