A quantitative analysis on the pricing of forward starting options under stochastic volatility and stochastic interest … and the stochastic volatility: compared to vanilla options, dynamic structures such as forward starting options are much … more sensitive to model specifications such as volatility, interest rate and correlation movements. We conclude that it is …

then apply a similar analysis to a time-dependent Heston stochastic volatility model, and we show to construct a time …-dependent mean reversion and volatility-of-variance function, so as to be consistent with the observed variance swap curve and a pre … second moments of the integrated variance, and derive an approximation for the price of a volatility swap under the time …

In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in … implied volatility function. The proof is based on saddlepoint methods and classical properties of holomorphic functions …