First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process

In this paper, an approximate version of the Barndorff-Nielsen and Shephard model, driven by a Brownian motion and a L\'evy subordinator, is formulated. The first-exit time of the log-return process for this model is analyzed. It is shown that with certain probability, the first-exit time process of the log-return is decomposable into the sum of the first exit time of the Brownian motion with drift, and the first exit time of a L\'evy subordinator with drift. Subsequently, the probability density functions of the first exit time of some specific L\'evy subordinators, connected to stationary, self-decomposable variance processes, are studied. Analytical expressions of the probability density function of the first-exit time of three such L\'evy subordinators are obtained in terms of various special functions. The results are implemented to empirical S&P 500 dataset.Comment: 27 pages, 7 figure

Some asymptotics for short maturity Asian options

Most of the existing methods for pricing Asian options are less efficient in the limit of small maturities and small volatilities. In this paper, we use the large deviations theory for the analysis of short-maturity Asian options. We present a local volatility model for the underlying market that incorporates a jump term in addition to the drift and diffusion terms. We estimate the asymptotics for the out-of-the-money, in-the-money, and at-the-money short-maturity Asian call and put options. Under appropriate assumptions, we show that the asymptotics for out-of-the-money Asian call and put options are governed by rare events. For the at-the-money Asian options, the result is more involved and in that case, we find the upper and lower bounds of the asymptotics of the Asian option price

Analysis of optimal portfolios on finite and small-time horizons for a multi-dimensional correlated stochastic volatility model

In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton-Jacobi-Bellman equation including the scaled covariances between the standard Brownian motions. We use an approximation method for the optimization of portfolios. With such approximation, the value function is analyzed using the first-order terms of expansion of the utility function in the powers of time to the horizon. The error of this approximation is controlled using the second-order terms of expansion of the utility function. It is also shown that the one-dimensional version of this analysis corresponds to a known result in the literature. We also generate a close-to-optimal portfolio near the time to horizon using the first-order approximation of the utility function. It is shown that the error is controlled by the square of the time to the horizon. Finally, we provide an approximation scheme to the value function for all times and generate a close-to-optimal portfolio.Comment: arXiv admin note: text overlap with arXiv:2104.0629

Role of Pilot Study in Assessing Viability of New Technology Projects: The Case of RFID in Parking Operations

The use of pilot studies to evaluate the economic justification of technology projects is common in practice. The pilot studies play even greater role in the projects affecting customer interactions with the product/service offerings since perception and/or reaction of customers is captured and analyzed through such studies. Yet, many times the methodology used in these studies lacks rigor and comprehensiveness, and there are scopes for further improvement. The current literature provides limited information on how the pilot studies should be used to decide whether to go ahead with a proposed technology project or not. In this paper we present guidelines for effectively using pilot studies in making such decisions. With the help of a real-life pilot study on deployment of RFID technology in parking operations at a university, we discuss how the proposed guidelines may be implemented to evaluate the cost-effectiveness of the proposed project. In recent times RFID technology is getting increasing attention and many organizations are in the process of deploying this technology. The paper offers a timely and cost-effective evaluation study of a particular application of RFID technology. We found that users’ benefits and costs played a crucial role in determining whether the proposed project should go forward or not. Also, we found that intangible benefits and costs to be important. These findings along with our discussions on the general methodology will provide practical guidelines for evaluating viability of technology projects using pilot studies