Designing catastrophic bonds for catastrophic risks in agriculture

2015 ◽  
Vol 75 (1) ◽  
pp. 47-62 ◽  
Author(s):  
Lin Sun ◽  
Calum G. Turvey ◽  
Robert A. Jarrow
Keyword(s):  
Monte Carlo ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Bond Price ◽  
Content Type ◽  
Catastrophe Bonds ◽  
Monte Carlo Techniques ◽  
Valuation Model ◽  
Cat Bonds

Purpose – The purpose of this paper is to outline a pricing formula for the valuation of catastrophic (CAT) bonds as applied to multiple trigger drought risks in Kenya. Design/methodology/approach – The valuation model is designed around the multiple triggers of the Mexican Catastrophe bonds, but the valuation model is based on Jarrow’s (2010) closed form CAT Bond Pricing model. The authors outline the model structure, the multiple tranches with rainfall triggers, and simulate the model using Monte Carlo methods. Data input was synthesized from historical rainfall data in Kenya’s Moyale region as well as prevailing LIBOR and rates and conventional coupons. Findings – The authors compute the valuation model using Monte Carlo techniques. The authors found the pricing method to be robust and consistent under various parameter settings including trigger levels, time after launch, recovery rates, coupon spreads, and zero coupon curves. For example the higher the trigger rates, the lower will be the bond price at issue. With 50 percent recovery the CAT bond at issue would be around $702 with a high triggers and 976 with low triggers, but the valuation changes with parameters. Practical implications – As far as the authors know the use of multiple trigger CAT bonds has been very limited in practice. The valuation formula and methods outlined in this paper show how CAT bonds can be effectively designed to address CAT covariate risks in developing agricultural economies. Originality/value – This paper examines CAT bonds to investigate multi-trigger rainfall risks in Kenya. The paper shows how CAT bonds can be designed to meet specific and CAT risks. Using Jarrow’s (2010) closed form solution this paper is one of the first to apply it to the macro-management of agricultural risks.

A closed-form solution to eye-to-hand calibration towards visual grasping

2014 ◽  
Vol 41 (6) ◽  
pp. 567-574 ◽  
Author(s):  
Hui Pan ◽  
Na Li Wang ◽  
Yin Shi Qin
Keyword(s):  
Closed Form ◽  
Design Methodology ◽  
Closed Form Solution ◽  
Form Solution ◽  
Content Type ◽  
The Impact ◽  
Calibration Plane

Purpose – The purpose of this paper is to propose a method that calibrates the hand-eye relationship for eye-to-hand configuration and afterwards a rectification to improve the accuracy of general calibration. Design/methodology/approach – The hand-eye calibration of eye-to-hand configuration is summarized as a equation AX = XB which is the same as in eye-in-hand calibration. A closed-form solution is derived. To abate the impact of noise, a rectification is conducted after the general calibration. Findings – Simulation and actual experiments confirm that the accuracy of calibration is obviously improved. Originality/value – Only a calibration plane is required for the hand-eye calibration. Taking the impact of noise into account, a rectification is carried out after the general calibration and, as a result, that the accuracy is obviously improved. The method can be applied in many actual applications.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

A CLOSED-FORM PRICING FORMULA FOR EUROPEAN EXCHANGE OPTIONS WITH STOCHASTIC VOLATILITY

2021 ◽  
pp. 1-10
Author(s):  
Puneet Pasricha ◽  
Anubha Goel
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stochastic Volatility Model ◽  
Strike Price ◽  
Volatility Model ◽  
Exchange Options ◽  
Pricing Formula ◽  
Exchange Option

This article derives a closed-form pricing formula for the European exchange option in a stochastic volatility framework. Firstly, with the Feynman–Kac theorem's application, we obtain a relation between the price of the European exchange option and a European vanilla call option with unit strike price under a doubly stochastic volatility model. Then, we obtain the closed-form solution for the vanilla option using the characteristic function. A key distinguishing feature of the proposed simplified approach is that it does not require a change of numeraire in contrast with the usual methods to price exchange options. Finally, through numerical experiments, the accuracy of the newly derived formula is verified by comparing with the results obtained using Monte Carlo simulations.

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