Pricing weather derivatives with the market price of risk extracted from the utility indifference valuation

2020 ◽  
Vol 79 (12) ◽  
pp. 3394-3409 ◽  
Author(s):  
Peng Li ◽  
Xiaoping Lu ◽  
Song-Ping Zhu
2012 ◽  
Vol 2 (4) ◽  
pp. 309-325 ◽  
Author(s):  
Jiwoon Kim ◽  
Dongwoo Sheen ◽  
Sungwon Shin

Abstract.This article analyses temperature data for Seoul based on a well defined daily average temperature (DAT) derived from records dating from 1954 to 2009, and considers related weather derivatives using a previous methodology. The temperature data exhibit some quite distinctive features, compared to other cities that have been considered before. Thus Seoul has: (i) four clear seasons; (ii) a significant seasonal range, with high temperature and humidity in the summer but low temperature and very dry weather in winter; and (iii) cycles of three cold days and four warmer days in winter. Due to these characteristics, seasonal variance and oscillation in Seoul is more apparent in winter and less evident in summer than in the other cities. We construct a deterministic model for the average temperature and then simulate future weather patterns, before pricing various weather derivative options and calculating the market price of risk (MPR).


Author(s):  
Flavio Angelini ◽  
Katia Colaneri ◽  
Stefano Herzel ◽  
Marco Nicolosi

AbstractWe study the optimal asset allocation problem for a fund manager whose compensation depends on the performance of her portfolio with respect to a benchmark. The objective of the manager is to maximise the expected utility of her final wealth. The manager observes the prices but not the values of the market price of risk that drives the expected returns. Estimates of the market price of risk get more precise as more observations are available. We formulate the problem as an optimization under partial information. The particular structure of the incentives makes the objective function not concave. Therefore, we solve the problem by combining the martingale method and a concavification procedure and we obtain the optimal wealth and the investment strategy. A numerical example shows the effect of learning on the optimal strategy.


Author(s):  
Tomas Björk

In this chapter we study a very general multidimensional Wiener-driven model using the martingale approach. Using the Girsanov Theorem we derive the martingale equation which is used to find an equivalent martingale measure. We provide conditions for absence of arbitrage and completeness of the model, and we discuss hedging and pricing. For Markovian models we derive the relevant pricing PDE and we also provide an explicit representation formula for the stochastic discount factor. We discuss the relation between the market price of risk and the Girsanov kernel and finally we derive the Hansen–Jagannathan bounds for the Sharpe ratio.


Author(s):  
Tomas Björk

We discuss market incompleteness within the relatively simple framework of a factor model. The corresponding pricing PDE is derived and we relate it to the market price of risk.


2006 ◽  
Vol 79 (5) ◽  
pp. 2337-2359 ◽  
Author(s):  
Jun Liu ◽  
Francis A. Longstaff ◽  
Ravit E. Mandell

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