The pricing of lookback options and binomial approximation

Refining a discrete model of Cheuk and Vorst, we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to infinity, thereby solving a problem posed by Lin and Palmer. We prove, in particular, that the price in the discrete model tends to the price in the continuous Black–Scholes model. Our results are based on an asymptotic expansion of the binomial cumulative distribution function that improves several recent results in the literature.     

ON‐THE‐JOB SEARCH,PRODUCTIVITY SHOCKS,AND THE INDIVIDUAL EARNINGS PROCESS*

Individual labor earnings observed in worker panel data have complex, highly persistent dynamics. We investigate the capacity of a structural job search model with on‐the‐job search, wage renegotiation by mutual consent, and i.i.d. productivity shocks to replicate salient properties of these dynamics, such as the covariance structure of earnings, the evolution of individual earnings mean, and variance with the duration of uninterrupted employment, or the distribution of year‐to‐year earnings changes. Structural estimation of our model on a 12‐year panel of highly educated British workers shows that our simple framework produces a dynamic earnings structure that is remarkably consistent with the data.     

Optimal high-frequency trading with limit and market orders

We propose a framework for studying optimal market-making policies in a limit order book (LOB). The bid–ask spread of the LOB is modeled by a tick-valued continuous-time Markov chain. We consider a small agent who continuously submits limit buy/sell orders at best bid/ask quotes, and may also set limit orders at best bid (resp. ask) plus (resp. minus) a tick for obtaining execution order priority, which is a crucial issue in high-frequency trading. The agent faces an execution risk since her limit orders are executed only when they meet counterpart market orders. She is also subject to inventory risk due to price volatility when holding the risky asset. The agent can then also choose to trade with market orders, and therefore obtain immediate execution, but at a less favorable price. The objective of the market maker is to maximize her expected utility from revenue over a short-term horizon by a trade-off between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/impulse control problem that we characterize in terms of a quasi-variational system by dynamic programming methods. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. We provide an explicit backward splitting scheme for solving the problem and show how it can be reduced to a system of simple equations involving only the inventory and spread variables. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market orders.     

A cost analysis of SIR-Spheres yttrium-90 resin microspheres versus tyrosine kinase inhibitors in the treatment of unresectable hepatocellular carcinoma in France,Italy, Spain and the UK

Abstract

Background and aims: A wide range of treatment options are available for hepatocellular carcinoma (HCC), including systemic treatment with tyrosine kinase inhibitors (TKIs) such as sorafenib and lenvatinib, immunotherapies, locoregional therapies such as selective internal radiation therapy (SIRT) and treatments with curative intent such as resection, radiofrequency ablation and liver transplantation. Given the substantial economic burden associated with HCC treatment, the aim of the present analysis was to establish the cost of using SIRT with SIR-Spheres yttrium-90 (Y-90) resin microspheres versus TKIs from healthcare payer perspectives in France, Italy, Spain and the United Kingdom (UK).

Methods: A cost model was developed to capture the costs of initial systemic treatment with sorafenib (95%) or lenvatinib (5%) versus SIRT in patients with HCC in Barcelona Clinic Liver Cancer (BCLC) stages B and C. A nested Markov model was utilized to model transitions between progression-free survival (PFS), progression and death, in addition to transitions between subsequent treatment lines. Cost and resource use data were identified from published sources in each of the four countries.

Results: Relative to TKIs, SIRT with SIR-Spheres Y-90 resin microspheres were found to be cost saving in all four country settings, with the additional costs of the microspheres and the SIRT procedure being more than offset by reductions in drug and drug administration costs, and treatment of adverse events. Across the four country settings, total cost savings with SIR-Spheres Y-90 resin microspheres fell within the range 5.4–24.9% and SIRT resulted in more patients ultimately receiving treatments with curative intent (4.6 vs. 1.4% of eligible patients).

Conclusion: SIR-Spheres Y-90 resin microspheres resulted in cost savings relative to TKIs in the treatment of unresectable HCC in all four country settings, while increasing the proportion of patients who become eligible for treatments with curative intent.     

AN EQUILIBRIUM SEARCH MODEL OF SYNCHRONIZED SALES*

We demonstrate the existence of periodic nonstationary equilibria with self‐generating cycles in a simple model of random search. Our results provide a theory of synchronized sales based on product market search by heterogeneous consumers. That is, our model explains how it can be optimal for all sellers to follow a repeated pattern of posting a high price for several periods and then posting a low price for one period.     

Beyond the personal–anonymous divide: agency relations in powers of attorney in France in the eighteenth and nineteenth centuries

Powers of attorney are often interpreted as evidence of trust among the parties involved. We build a novel dataset of notarized powers of attorney, capturing a wide variety of agency relationships in four large French commercial cities in the eighteenth and nineteenth centuries, to test hypotheses on the relational basis of economic relationships. We find little support for the idea of a radical shift from personal to anonymous relationships during our period. Our results point to more nuanced transformations. The preference for proxies in the same occupation as the principal somewhat declined, while professional proxies emerged and principals used relational chains, especially involving notaries, to find proxies.     

Model-free stochastic collocation for an arbitrage-free implied volatility: Part I

This paper explains how to calibrate a stochastic collocation polynomial against market option prices directly. The method is first applied to the interpolation of short-maturity equity option prices in a fully arbitrage-free manner and then to the joint calibration of the constant maturity swap convexity adjustments with the interest rate swaptions smile. To conclude, we explore some limitations of the stochastic collocation technique.

     

Jingle bells or ‘green’ bells? The impact of socially responsible consumption principles upon consumer behaviour at Christmas time

Socially responsible consumption (SRC) behaviours have progressed over the last few years and appear to show signs of a lasting trend. Situations of atypical consumption such as Christmas time, however, raise an important and as of yet unexplored question: What are the influences of unusual situations upon the relationship between people's socially responsible profile and their socially responsible purchase intentions (SRPI)? The objective of this article is thus to use the theory of planned behaviour (Ajzen, 1991 ) and environment‐based variables, called ‘atmospherics’, to answer to this question. A Web survey on a total sample of 301 Canadian consumers, shows that people's past SRC behaviours are positively related to their SRPI in unusual situations. Moreover, the atmosphere of the place consumers are situated in has a negative moderating influence upon this relationship. This result is explained by a change in people's attitude toward SRC. However, this negative moderating effect of atmosphere is contained and constrained by social desirability in the form of subjective norms on SRC and the level of behavioural control consumers perceive.     

Accounting for endogeneity in matching function estimation

We show that equilibrium matching models imply that standard estimates of the matching function elasticities are exposed to an endogeneity bias, which arises from the search behavior of agents on either side of the market. We offer an estimation method which, under certain structural assumptions about the process driving shocks to matching efficiency, is immune from that bias. Application of our method to the estimation of a basic version of the matching function using aggregate U.S. data from the Job Openings and Labor Turnover Survey (JOLTS) suggests that the bias can be quantitatively important.