This paper considers asset price dynamics of which discounted return is modeled by a multi-dimensional affine diffusion process . By analyzing the Riccati system, which is associated with the affine process via the transform formula, we fully characterize the regions of exponents in which asset price moments do not explode at any time or explode at a given time. These behaviors are closely tied to the long-term growth rate of asset price momentsas well as implied volatility asymptotics at large-time-to-maturity or at extreme strikes for any given option maturity .
This paper considers multi-dimensional affine processes with continuous sample paths . By analyzing the Riccati system, which is associated with the affine process via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode at a given time. In these two cases, we also compute the long-term growth rate and the explosion rate for exponential moments. These results provide a handle to study implied volatility asymptotics in models where return of stock prices are modeled by affine processes whose exponential moments do not have an explicit formula .
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asset price dynamics of which discounted return is modeled by a
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diffusion process
processes with continuous sample paths
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asset price moments
exponential moments of a given process
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These behaviors are closely tied to
In these two cases, we also compute
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of asset price momentsas well as
and the explosion rate for exponential moments. These results provide a handle to study
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at large-time-to-maturity or at extreme strikes for any given option maturity
in models where return of stock prices are modeled by affine processes whose exponential moments do not have an explicit formula