TY - JOUR
T1 - Stochastic volatility
T2 - Option pricing using a multinomial recombining tree
AU - Florescu, Ionut
AU - Viens, Frederi G.
PY - 2008/4
Y1 - 2008/4
N2 - The problem of option pricing is treated using the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be mean-reverting. Assuming that only discrete past stock information is available, an interacting particle stochastic filtering algorithm due to Del Moral et al. (Del Moral et al., 2001) is adapted to estimate the SV, and a quadrinomial tree is constructed which samples volatilities from the SV filter's empirical measure approximation at time 0. Proofs of convergence of the tree to continuous-time SV models are provided. Classical arbitrage-free option pricing is performed on the tree, and provides answers that are close to market prices of options on the SP500 or on blue-chip stocks. Results obtained here are compared with those from non-random volatility models, and from models which continue to estimate volatility after time 0. It is shown precisely how to calibrate the incomplete market, choosing a specific martingale measure, by using a benchmark option.
AB - The problem of option pricing is treated using the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be mean-reverting. Assuming that only discrete past stock information is available, an interacting particle stochastic filtering algorithm due to Del Moral et al. (Del Moral et al., 2001) is adapted to estimate the SV, and a quadrinomial tree is constructed which samples volatilities from the SV filter's empirical measure approximation at time 0. Proofs of convergence of the tree to continuous-time SV models are provided. Classical arbitrage-free option pricing is performed on the tree, and provides answers that are close to market prices of options on the SP500 or on blue-chip stocks. Results obtained here are compared with those from non-random volatility models, and from models which continue to estimate volatility after time 0. It is shown precisely how to calibrate the incomplete market, choosing a specific martingale measure, by using a benchmark option.
KW - Incomplete markets
KW - Monte Carlo method
KW - Option pricing
KW - Options market
KW - Particle method
KW - Random tree
KW - Stochastic filtering
KW - Stochastic volatility
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U2 - 10.1080/13504860701596745
DO - 10.1080/13504860701596745
M3 - Article
AN - SCOPUS:40949160600
SN - 1350-486X
VL - 15
SP - 151
EP - 181
JO - Applied Mathematical Finance
JF - Applied Mathematical Finance
IS - 2
ER -