Stochastic Volatility for Lévy Processes

Three processes reflecting persistence of volatility are initially formulated by evaluating three Lévy processes at a time change given by the integral of a mean-reverting square root process. The model for the mean-reverting time change is then generalized to include non-Gaussian models that are solutions to Ornstein-Uhlenbeck equations driven by one-sided discontinuous Lévy processes permitting correlation with the stock. Positive stock price processes are obtained by exponentiating and mean correcting these processes, or alternatively by stochastically exponentiating these processes. The characteristic functions for the log price can be used to yield option prices via the fast Fourier transform. In general mean-corrected exponentiation performs better than employing the stochastic exponential. It is observed that the mean-corrected exponential model is not a martingale in the filtration in which it is originally defined. This leads us to formulate and investigate the important property of martingale marginals where we seek martingales in altered filtrations consistent with the one-dimensional marginal distributions of the level of the process at each future date.     

Option Pricing With V. G. Martingale Components1

European call options are priced when the uncertainty driving the stock price follows the V. G. stochastic process (Madan and Seneta 1990). the incomplete markets equilibrium change of measure is approximated and identified using the log return mean, variance, and kurtosis. an exact equilibrium interpretation is also provided, allowing inference about relative risk aversion coefficients from option prices. Relative to Black-Scholes, V. G. option values are higher, particularly so for out of the money options with long maturity on stocks with high means, low variances, and high kurtosis.     

Pricing Reinsurance Contracts on FDIC Losses

This paper proposes a pricing model for the FDIC's reinsurance risk. We derive a closed‐form Weibull call option pricing model to price a call‐spread a reinsurer might sell to the FDIC. To obtain the risk‐neutral loss‐density necessary to price this call spread we risk‐neutralize a Weibull distributed FDIC annual losses by a tilting coefficient estimated from the traded call options on the BKX index. An application of the proposed approach yield reasonable reinsurance prices.     

Toward a Fine Balance: Cross-Cultural Comparison of Work–Family Identities

This study investigates the differences in the salience of work and family identities between samples of employees in the United States and India. The authors hypothesized the effects of cultural differences on these workers' salient identities. Additionally, the authors hypothesized that across cultures a balance in the importance of family and work identities achieved by an individual would lead to greater job and life satisfaction and fewer intentions to turnover. Structural equation modeling tests support the authors' hypotheses. This article contributes toward an understanding of cross-cultural differences and even some similarities in work–family identity issues and the outcomes a balance in them engender.     

Community Connections to Enhance Undergraduate International Business Education: An Example of Business Consulting Projects

Practical project experience as a means of augmenting traditional classroom learning has long been viewed as a value adding curricular exercise. While students participating in the projects gain valuable skills that will enhance their personal marketability, successful projects also benefit the client companies involved and help enhance the image of the university. Substantial effort goes into planning and implementing such an experience and involves extensive coordination with multiple constituents. This article details how a project-based capstone experience was developed in partnership with the local business community and the College's Center for International Business as part of the degree requirements for a relatively new Bachelor of Science in International Business program.     

Machine learning for quantitative finance: fast derivative pricing,hedging and fitting

In this paper, we show how we can deploy machine learning techniques in the context of traditional quant problems. We illustrate that for many classical problems, we can arrive at speed-ups of several orders of magnitude by deploying machine learning techniques based on Gaussian process regression. The price we have to pay for this extra speed is some loss of accuracy. However, we show that this reduced accuracy is often well within reasonable limits and hence very acceptable from a practical point of view. The concrete examples concern fitting and estimation. In the fitting context, we fit sophisticated Greek profiles and summarize implied volatility surfaces. In the estimation context, we reduce computation times for the calculation of vanilla option values under advanced models, the pricing of American options and the pricing of exotic options under models beyond the Black–Scholes setting.     

Factor Models for Option Pricing

Options on stocks are priced using information on index options and viewing stocks in a factor model as indirectly holding index risk. The method is particularly suited to developing quotations on stock options when these markets are relatively illiquid and one has a liquid index options market to judge the index risk. The pricing strategy is illustrated on IBM and Sony options viewed as holding SPX and Nikkei risk respectively.     

Leveraged Lévy processes as models for stock prices

Adopting a constant elasticity of variance formulation in the context of a general Lévy process as the driving uncertainty we show that the presence of the leverage effect? ?One explanation of the documented negative relation between market volatilities and the level of asset prices (the ‘smile’ or ‘skew’), we term the ‘leverage effect’, argues that this negative relation reflects greater risk taking by the management, induced by a fall in the asset price, with a view of maximizing the option value of equity shareholders. in this form has the implication that asset price processes satisfy a scaling hypothesis. We develop forward partial integro-differential equations under a general Markovian setup, and show in two examples (both continuous and pure-jump Lévy) how to use them for option pricing when stock prices follow our leveraged Lévy processes. Using calibrated models we then show an example of simulation-based pricing and report on the adequacy of using leveraged Lévy models to value equity structured products.