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A remark on Gatheral's 'most-likely path approximation' of implied volatility
remark on Gatheral's 'most-likely path implied volatility
2010/11/2
We give a rigorous proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we fix the problem of a circular defi...
Asymptotic Implied Volatility at the Second Order with Application to the SABR Model
Stochastic volatility Asymptotic expansion Heat kernel
2010/11/1
We provide a general method to compute a Taylor expansion in time of implied volatility for
stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is...
Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes
Call and put pricing functions Implied volatility Asymptotic formulas Pareto-type distributions Regularly varying functions
2010/11/1
In this paper, we obtain asymptotic formulas with error estimates for the implied volatility
associated with a European call pricing function. We show that these formulas imply Lee’s moment formulas ...