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[CT177]

Session Date & Time : 1C (Aug.21, 13:20-15:00)
Type : Contributed Talk
Abstract : We present a non-probabilistic, pathwise approach to continuous-time finance based on causal functional calculus. We introduce a definition of self-financing, free from any integration concept and show that the value of a self-financing portfolio is a pathwise integral and that generic domain of functional calculus is inherently arbitrage-free. We then consider the problem of hedging a path-dependent payoff across a generic set of scenarios. We apply the transition principle of Isaacs in differential games and obtain a verification theorem for the optimal solution, which is characterised by a fully non-linear path-dependent equation. For the Asian option, we obtain explicit solution.
Classification : 91G99, 91-10, Mathematical finance in continuous-time, model uncertainty
Author(s) :
- Henry Chiu (Imperial College London)

Session Date & Time : 1C (Aug.21, 13:20-15:00)
Type : Contributed Talk
Abstract : This paper considers approximate-analytical solutions of a time-space-fractional one-factor commodity pricing model using a coupled technique termed Fractional-Complex-Transform with the aid of Banach Contraction Principle. The fractional derivatives are defined in Jumarie’s sense Some noteworthy remarks are made in comparison to the solutions of the model in its classical integer form. Consequently, the proposed novel method is suggested for the solutions of other complex financial models, including multi-factor and non-linear models.
Classification : 91GXX, 37NXX, option pricing
Author(s) :
- Sunday Onos EDEKI (Department of Mathematics, Covenant University)

Session Date & Time : 1C (Aug.21, 13:20-15:00)
Type : Contributed Talk
Abstract : This paper analyses the attributes and the significance of the roughness of oil market volatil- ity. We employ unspanned stochastic volatility models driven by rough Brownian motions that yield semi-analytic prices for futures options entailing efficient calibration applications. We calibrate option prices written on oil futures and provide empirical evidence of the dy- namic nature of the roughness in oil volatility. The calibrated option-implied Hurst param- eter varies over time, but rough stochastic volatility models provide a better fit to the term structure of implied oil volatility compared to classical stochastic volatility. Furthermore, including the Hurst parameter into the set of implied parameters benefits the stability of the calibrated parameters and improves pricing performance.
Classification : 91Gxx, 60Lxx, 60Hxx
Author(s) :
- Christina Nikitopoulos (UTS)
- Messias Alfeus (Stellenbosch University)
- Ludger Overbeck (Justus-Liebig-University Giessen)