prices caused by stochastic volatility. -- option pricing ; autoregression ; heteroskedasticity ; GARCH ; leverage effect …

) and volatility (Theorem 2) swaps for stochastic volatilities driven by the semi-Markov processes. We also discuss some … extensions of the obtained results such as local semi-Markov volatility, Dupire formula for the local semi-Markov volatility and …

We introduce an asymptotic expansion for forward start options in a multi-factor local-stochastic volatility model. We … derive explicit approximation formulas for the so-called forward implied volatility which can be useful to price complex path … generalized to a wider class of local-stochastic volatility models. We illustrate the effectiveness of the technique through some …

one-month variance swap rate, i.e., the CBOE Volatility Index (VIX) accurately. Our research suggests that one should use …

diffusive volatility and squared jump variation. We use this result to develop a new option valuation model in which the … underlying asset price exhibits volatility and jump intensity dynamics. The volatility and jump intensity dynamics in the model … are directly driven by model-free empirical measures of diffusive volatility and jump variation. Because the empirical …

maturity. Using this result, we then derive the implied volatility in the large-time limit in the new regime, and we find that … volatility smile does not flatten out as the maturity increases, but rather it spreads out, and the large-time, large … for the implied volatility in the usual large-time, fixed-strike regime, at leading order. We find that there are two …

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 …