“Influence of Price Elasticity of Demand on Monopoly Games under Different Returns to Scale” joint with Xiaoliang Li and Jing Yang, (Forthcoming in Mathematics and Computers in Simulation)

Abstract:
This paper examines a monopoly market featured by a general isoelastic demand function. Assuming that the monopolist’s cost function is quadratic, we investigate the influence of the price elasticity of demand on the behavior of monopoly games under various (decreasing, constant, and increasing) returns to scale. Note that the assumption of a general isoelastic demand function and a quadratic cost function results in the equilibrium equation becoming transcendental, which makes the closed-form solutions unattainable. To overcome this obstacle, we adopt an innovative approach that utilizes the special structure of the marginal revenue and the marginal cost to conduct the comparative static analysis and the stability analysis. This paper also introduces two boundedly rational dynamic models based on different (gradient and LMA) mechanisms of adjusting the output. Our findings reveal that the LMA model is more stable in both the parameter space and the state space than the gradient model. In particular, it is proved that the unique non-vanishing equilibrium of the LMA model is globally asymptotically stable.

Available at SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4945483

“How Much is the Gap? — Efficient Overnight Jump Risk-Adjusted Valuation of Leveraged Certificates” (2017), Quantitative Finance, Vol. 17, No. 9, pp. 1387-1401, joint with Matthias Thul

Abstract:
This paper develops a novel and highly efficient numerical algorithm for the gap risk-adjusted valuation of leveraged certificates. The existing literature relies exclusively on Monte Carlo simulations for this purpose. These are not sufficiently fast to be used in a market making environment where issuers need to compute thousands of price updates per second. By valuing leveraged certificates as multi-window barrier options, we explicitly model jumps that occur at deterministically known times, such as between the exchange closing and re-opening. Our algorithm combines the one-day transition probability with Simpson’s numerical integration rule. This yields a backward induction scheme that requires a significantly coarser spacial and time grid than finite difference methods. We demonstrate its robustness and accuracy through Monte Carlo simulations.

Published version: http://www.tandfonline.com/doi/full/10.1080/14697688.2016.1276299
Preprint available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2388734

Presented or Accepted for Presentation at:

• 9th World Congress of the Bachelier Finance Society, July 2016, New York