Pricing Options On Risky Assets In A Stochastic Interest Rate Economy 1

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73150/1/j.1467-9965.1992.tb00030.x.pd

Local time and the pricing of time-dependent barrier options

A time-dependent double-barrier option is a derivative security that delivers the terminal value $\phi(S_T)$ at expiry $T$ if neither of the continuous time-dependent barriers b_\pm:[0,T]\to \RR_+ have been hit during the time interval $[0,T]$. Using a probabilistic approach we obtain a decomposition of the barrier option price into the corresponding European option price minus the barrier premium for a wide class of payoff functions $\phi$, barrier functions $b_\pm$ and linear diffusions $(S_t)_{t\in[0,T]}$. We show that the barrier premium can be expressed as a sum of integrals along the barriers $b_\pm$ of the option's deltas \Delta_\pm:[0,T]\to\RR at the barriers and that the pair of functions $(\Delta_+,\Delta_-)$ solves a system of Volterra integral equations of the first kind. We find a semi-analytic solution for this system in the case of constant double barriers and briefly discus a numerical algorithm for the time-dependent case.Comment: 32 pages, to appear in Finance and Stochastic

Measuring Market Liquidity Risk - Which Model Works Best?

Market liquidity risk, the difficulty or cost of trading assets in crises, has been recognized as an important factor in risk management. Literature has already proposed several models to include liquidity risk in the standard Value-at-Risk framework. While theoretical comparisons between those models have been conducted, their empirical performance has never been benchmarked. This paper performs comparative back-tests of daily risk forecasts for a large selection of traceable liquidity risk models. In a 5.5 year stock sample we show which model provides most accurate results and provide detailed recommendations which model is most suitable in a specific situation

Efficient pricing of ratchet equity-indexed annuities in a variance-gamma economy

In this paper we propose a new method for approximating the price of arithmetic Asian options in a Variance-Gamma (VG) economy, which is then applied to the problem of pricing equityindexed annuity contracts. The proposed procedure is an extension to the case of a VG-based model of the moment-matching method developed by Turnbull and Wakeman and Levy for the pricing of this class of path-dependent options in the traditional Black-Scholes setting. The accuracy of the approximation is analyzed against RQMC estimates for the case of ratchet equityindexed annuities with index averaging

Measuring and managing liquidity risk in the Hungarian practice

The crisis that unfolded in 2007/2008 turned the attention of the financial world toward liquidity, the lack of which caused substantial losses. As a result, the need arose for the traditional financial models to be extended with liquidity. Our goal is to discover how Hungarian market players relate to liquidity. Our results are obtained through a series of semistructured interviews, and are hoped to be a starting point for extending the existing models in an appropriate way. Our main results show that different investor groups can be identified along their approaches to liquidity, and they rarely use sophisticated models to measure and manage liquidity. We conclude that although market players would have access to complex liquidity measurement and management tools, there is a limited need for these, because the currently available models are unable to use complex liquidity information effectively