1,528 research outputs found
Option Pricing with Orthogonal Polynomial Expansions
We derive analytic series representations for European option prices in
polynomial stochastic volatility models. This includes the Jacobi, Heston,
Stein-Stein, and Hull-White models, for which we provide numerical case
studies. We find that our polynomial option price series expansion performs as
efficiently and accurately as the Fourier transform based method in the nested
affine cases. We also derive and numerically validate series representations
for option Greeks. We depict an extension of our approach to exotic options
whose payoffs depend on a finite number of prices.Comment: forthcoming in Mathematical Finance, 38 pages, 3 tables, 7 figure
Modelling FX smile : from stochastic volatility to skewness
Imperial Users onl
Interest rate models with Markov chains
Imperial Users onl
Maximum Likelihood Estimation of Stochastic Volatility Models
We develop and implement a new method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by the implied volatility of a short dated at-the-money option. We find that the approximation results in a negligible loss of accuracy. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine model of Heston (1993) and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.
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