Convergence of subdifferential under strong stochastic convexity

Article Abstract:

A convergence property of subgradients of sequences of stochastically convex functions is considered. It is shown that a case in which a sequence of random functions that has a strong stochastic convexity with respect to a parameter and that converges pointwise with probability one will result in a convergence between any sequence of elements from the subdifferentials of the functions in the sequence and the subdifferential of the limiting function at probability one. This analysis extends previous studies of Glynn, Yu and other researchers by not holding any differential assumption on the limiting function. One significant use of the convergence property of subdifferentials under strong stochastic convexity is in proving strong consistency of infinitesimal perturbation analysis.

Perturbation (Mathematics)

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Option pricing with stochastic volatility: information-time vs. calendar-time

Article Abstract:

Empirical evidence supports the proposition that stock market volatility is stochastic in calendar-time due to the random arrival of information and that it becomes stationary in information-time. A study is conducted to investigate the implication of this proposition on option pricing. A new approach to price options with stochastic volatility is developed, in which the underlying asset return follows a jump subordinated process and the options are priced in both calendar-time and information-time. The stochastic time change from calendar-time to information-time is intended to achieve a stationary underlying asset return process to option pricing. This time change is found to minimize the computational complexity of the option pricing problem.

Prices and rates, Stock-exchange, Stock exchanges, Options (Finance), Pricing

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