TY - JOUR
T1 - INTEGRAL REPRESENTATION of PROBABILITY DENSITY of STOCHASTIC VOLATILITY MODELS and TIMER OPTIONS
AU - Cui, Zhenyu
AU - Kirkby, J. Lars
AU - Lian, Guanghua
AU - Nguyen, Duy
N1 - Publisher Copyright:
© 2017 World Scientific Publishing Company.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - This paper contributes a generic probabilistic method to derive explicit exact probability densities for stochastic volatility models. Our method is based on a novel application of the exponential measure change in [Z. Palmowski & T. Rolski (2002) A technique for exponential change of measure for Markov processes, Bernoulli 8(6), 767-785]. With this generic approach, we first derive explicit probability densities in terms of model parameters for several stochastic volatility models with nonzero correlations, namely the Heston 1993, 3/2, and a special case of the α-Hypergeometric stochastic volatility models recently proposed by [J. Da Fonseca & C. Martini (2016) The α-Hypergeometric stochastic volatility model, Stochastic Processes and their Applications 126(5), 1472-1502]. Then, we combine our method with a stochastic time change technique to develop explicit formulae for prices of timer options in the Heston model, the 3/2 model and a special case of the α-Hypergeometric model.
AB - This paper contributes a generic probabilistic method to derive explicit exact probability densities for stochastic volatility models. Our method is based on a novel application of the exponential measure change in [Z. Palmowski & T. Rolski (2002) A technique for exponential change of measure for Markov processes, Bernoulli 8(6), 767-785]. With this generic approach, we first derive explicit probability densities in terms of model parameters for several stochastic volatility models with nonzero correlations, namely the Heston 1993, 3/2, and a special case of the α-Hypergeometric stochastic volatility models recently proposed by [J. Da Fonseca & C. Martini (2016) The α-Hypergeometric stochastic volatility model, Stochastic Processes and their Applications 126(5), 1472-1502]. Then, we combine our method with a stochastic time change technique to develop explicit formulae for prices of timer options in the Heston model, the 3/2 model and a special case of the α-Hypergeometric model.
KW - Stochastic volatility
KW - exact probability densities
KW - implied volatility
KW - timer option
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U2 - 10.1142/S0219024917500558
DO - 10.1142/S0219024917500558
M3 - Article
AN - SCOPUS:85038895904
SN - 0219-0249
VL - 20
JO - International Journal of Theoretical and Applied Finance
JF - International Journal of Theoretical and Applied Finance
IS - 8
M1 - 1750055
ER -