MOA-2019-BLG-008Lb : a new microlensing detection of an object at the planet/brown dwarf boundary

Funding: R.A.S. and E.B. gratefully acknowledge support from NASA grant 80NSSC19K0291. Y.T. and J.W. acknowledge the support of DFG priority program SPP 1992 “Exploring the Diversity of Extrasolar Planets” (WA 1047/11-1). K.H. acknowledges support from STFC grant ST/R000824/1. J.C.Y. acknowledges support from NSF grant No. AST-2108414. Work by C.H. was supported by the grants of the National Research Foundation of Korea (2019R1A2C2085965 and 2020R1A4A2002885). D.M.B. acknowledges the support of the NYU Abu Dhabi Research Enhancement Fund under grant RE124. This work was partly supported by the National Science Foundation of China (grant Nos. 11333003, 11390372, and 11761131004 to S.M.). The MOA project is supported by JSPS KAKENHI grant Nos. JSPS24253004, JSPS26247023, JSPS23340064, JSPS15H00781, JP16H06287, and JP17H02871.We report on the observations, analysis and interpretation of the microlensing event MOA-2019-BLG-008. The observed anomaly in the photometric light curve is best described through a binary lens model. In this model, the source did not cross caustics and no finite-source effects were observed. Therefore, the angular Einstein ring radius θE cannot be measured from the light curve alone. However, the large event duration, tE ∼ 80 days, allows a precise measurement of the microlensing parallax πE. In addition to the constraints on the angular radius θ* and the apparent brightness Is of the source, we employ the Besançon and GalMod galactic models to estimate the physical properties of the lens. We find excellent agreement between the predictions of the two galactic models: the companion is likely a resident of the brown dwarf desert with a mass Mp ∼ 30 MJup, and the host is a main-sequence dwarf star. The lens lies along the line of sight to the Galactic bulge, at a distance of ≤4 kpc. We estimate that in about 10 yr the lens and source will be separated by ∼55 mas, and it will be possible to confirm the exact nature of the lensing system by using high-resolution imaging from ground- or space-based observatories.Publisher PDFPeer reviewe

A Quasi-analytical Interpolation Method for Pricing American Options under General Multi-dimensional Diffusion Processes

We present a quasi-analytical method for pricing multi-dimensional American options based on interpolating two arbitrage bounds, along the lines of Johnson (1983). Our method allows for the close examination of the interpolation parameter on a rigorous theoretical footing instead of empirical regression. The method can be adapted to general diffusion processes as long as quick and accurate pricing methods exist for the corresponding European and perpetual American options. The American option price is shown to be approximately equal to an interpolation of two European option prices with the interpolation weight proportional to a perpetual American option. In the Black-Scholes model, our method achieves the same e±ciency as Barone-Adesi and Whaley's (1987) quadratic approximation with our method being generally more accurate for out-of-the-money and long-maturity options. When applied to Heston's stochastic volatility model, our method is shown to be extremely e±cient and fairly accurate