Comparing optimal convergence rate of stochastic mesh and least squares method for Bermudan option pricing

We analyze the stochastic mesh method (SMM) as well as the least squares method (LSM) commonly used for pricing Bermudan options using the standard two phase methodology. For both the methods, we determine the decay rate of mean square error of the estimator as a function of the computational budget allocated to the two phases and ascertain the order of the optimal allocation in these phases. We conclude that with increasing computational budget, while SMM estimator converges at a slower rate compared to LSM estimator, it converges to the true option value whereas LSM estimator, with fixed number of basis functions, usually converges to a biased value

Efficient simulation of large deviation events for sums of random vectors using saddle-point representations

We consider the problem of efficient simulation estimation of the density function at the tails, and the probability of large deviations for a sum of independent, identically distributed (i.i.d.), light-tailed and nonlattice random vectors. The latter problem besides being of independent interest, also forms a building block for more complex rare event problems that arise, for instance, in queuing and financial credit risk modeling. It has been extensively studied in the literature where state-independent, exponential-twisting-based importance sampling has been shown to be asymptotically efficient and a more nuanced state-dependent exponential twisting has been shown to have a stronger bounded relative error property. We exploit the saddle-point-based representations that exist for these rare quantities, which rely on inverting the characteristic functions of the underlying random vectors. These representations reduce the rare event estimation problem to evaluating certain integrals, which may via importance sampling be represented as expectations. Furthermore, it is easy to identify and approximate the zero-variance importance sampling distribution to estimate these integrals. We identify such importance sampling measures and show that they possess the asymptotically vanishing relative error property that is stronger than the bounded relative error property. To illustrate the broader applicability of the proposed methodology, we extend it to develop an asymptotically vanishing relative error estimator for the practically important expected overshoot of sums of i.i.d. random variables

American options under stochastic volatility: control variates, maturity randomization & multiscale asymptotics

American options are actively traded worldwide on exchanges, thus making their accurate and efficient pricing an important problem. As most financial markets exhibit randomly varying volatility, in this paper we introduce an approximation of American option price under stochastic volatility models. We achieve this by using the maturity randomization method known as Canadization. The volatility process is characterized by fast and slow scale fluctuating factors. In particular, we study the case of an American put with a single underlying asset and use perturbative expansion techniques to approximate its price as well as the optimal exercise boundary up to the first order. We then use the approximate optimal exercise boundary formula to price American put via Monte Carlo. We also develop efficient control variates for our simulation method using martingales resulting from the approximate price formula. A numerical study is conducted to demonstrate that the proposed method performs better than the least squares regression method popular in the financial industry, in typical settings where values of the scaling parameters are small. Further, it is empirically observed that in the regimes where scaling parameter value is equal to unity, fast and slow scale approximations are equally accurate

Efficient simulation of density and probability of large deviations of sum of random vectors using saddle point representations

We consider the problem of efficient simulation estimation of the density function at the tails, and the probability of large deviations for a sum of independent, identically distributed, light-tailed and non-lattice random vectors. The latter problem besides being of independent interest, also forms a building block for more complex rare event problems that arise, for instance, in queueing and financial credit risk modelling. It has been extensively studied in literature where state independent exponential twisting based importance sampling has been shown to be asymptotically efficient and a more nuanced state dependent exponential twisting has been shown to have a stronger bounded relative error property. We exploit the saddle-point based representations that exist for these rare quantities, which rely on inverting the characteristic functions of the underlying random vectors. These representations reduce the rare event estimation problem to evaluating certain integrals, which may via importance sampling be represented as expectations. Further, it is easy to identify and approximate the zero-variance importance sampling distribution to estimate these integrals. We identify such importance sampling measures and show that they possess the asymptotically vanishing relative error property that is stronger than the bounded relative error property. To illustrate the broader applicability of the proposed methodology, we extend it to similarly efficiently estimate the practically important expected overshoot of sums of iid random variables

Development of Neural Network Based Adaptive Change Detection Technique for Land Terrain Monitoring with Satellite and Drone Images

Role of satellite images is increasing in day-to-day life for both civil as well as defence applications. One of the major defence application while troop’s movement is to know about the behaviour of the terrain in advance by which smooth transportation of the troops can be made possible. Therefore, it is important to identify the terrain in advance which is quite possible with the use of satellite images. However, to achieve accurate results, it is essential that the data used should be precise and quite reliable. To achieve this with a satellite image alone is a challenging task. Therefore, in this paper an attempt has been made to fuse the images obtained from drone and satellite, to achieve precise terrain information like bare land, dense vegetation and sparse vegetation. For this purpose, a test area nearby Roorkee, Uttarakhand, India has been selected, and drone and Sentinel-2 data have been taken for the same dates. A neural network based technique has been proposed to obtain precise terrain information from the Sentinel-2 image. A quantitative analysis was carried out to know the terrain information by using change detection. It is observed that the proposed technique has a good potential to identify precisely bare land, dense vegetation, and sparse vegetation which may be quite useful for defence as well as civilian application

Impact of Social Media on Spiritual Tourism in India: An SEM analysis of the critical factors impacting on decision making

Over the last two decades, an exponential rise has been observed in the growth of spiritual tourism where travellers are preferring and visiting places of religious inclination seeking to align their body and mind. In the current fast paced life where stress, anxiety, insecurities and depression have become common place, travelling to certain places that provide connection with the almighty or peace to the traveller has become very important. Spiritual tourism in India has always been very highly valued and is active as an industry in a country known as the land of temples and gods. Many globally popular destinations exist in India that attract both domestic and international travellers alike. Destinations like Puri Jagannath, Kedarnath, Amarnath Yatra, Rishikesh, Varanasi, and Haridwar have developed their image and branding power over the years for the peace and meditating impact they have on their tourists. This trend has also been enhanced by the overall image of India as a country for religious and spiritual tourism where lakhs of international tourist come for relaxation and peace. The transformation of social media platforms has had an important and significant impact on the destination branding of spiritual locations and the final decision making of travellers. As travellers are active on social media platforms in sharing their stories of travel, sharing posts and videos, highlighting their travel, they are sharing their experiences with a large community. Thus, social media impacts on decision making for spiritual destinations needs to be studied in depth to understand the underlying factors that impact the final decision. For the purpose of this paper, various variables are analysed through the SEM framework to determine their interdependency and how they influence the final decision of the tourist. The study is important for academics in tourism as it discusses the most relevant examples and key factors. The study is also meaningful to practitioners of tourism who can ensure that the correct social media marketing can be undertaken for attracting tourists to spiritual destinations

IMECE2005-79066 SEMI-ACTIVE VIBRATION DAMPING BY MODULATION OF JOINT FRICTION

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Understanding the Role of Online Support to Tourist Spots in India

The online travel agencies or popularly known as OTAs have become one of the most reliable options for the travellers to make their arrangements. The number of players both across the world and in India have seen a rise and the same has quite successfully helped in planning trips for many tourists. The study here is curious to understand the role of these OTAs in the process of resuming the tourist destination especially in India. The situation in India with respect to the use of OTAs is quite different as the country is an emerging one and there are issues of digital divide still persistent in the economy The study here collected 238 primary responses from tourist across the country to identify their perception about the online travel agencies and recognise the factors that cause an impact in the adoption process. The study has used a number of advanced statistical methods such as principal component analyses and multiple linear regression to establish the factors as well as the relationship with the adoption process. The regression model being formulated is able to estimate of variance of 14% on the intention of using online modes to put the two responses in India by highlighting the two main factors causing an impact on it. The perceived ease of use and the information transparency are the main reasons why a tourist based in India prefers to book their destination requirements using online travel agencies