Modeling and Computation of CO2Allowance Derivatives Under Jump-Diffusion Processes

AbstractIn this paper, we study carbon emission trading whose market is gaining in popularity as a policy instrument for global climate change. The mathematical model is presented for pricing options on CO2emission allowance futures with jump diffusion processes, and a so-called fitted finite volume method is proposed to solve the pricing model for the spatial discretization, in which the Crank-Nicolson is employed for time stepping. In addition, the stability and the convergence of the fully discrete scheme are given, and some numerical results, which are compared with the closed form solution and the Monte Carlo simulation solution, are provided to demonstrate the rates of convergence and the robustness of the numerical method.

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THE VALUATION OF RUSSIAN OPTIONS FOR DOUBLE EXPONENTIAL JUMP DIFFUSION PROCESSES

Asia Pacific Journal of Operational Research ◽

10.1142/s021759591000265x ◽

2010 ◽

Vol 27 (02) ◽

pp. 227-242 ◽

Cited By ~ 3

Author(s):

ATSUO SUZUKI ◽

KATSUSHIGE SAWAKI

Keyword(s):

Value Function ◽

Diffusion Processes ◽

Closed Form Solution ◽

Jump Diffusion ◽

Form Solution ◽

Jump Diffusion Processes ◽

Double Exponential ◽

Analytical Properties ◽

Russian Option ◽

The Value Function

In this paper, we derive closed form solution for Russian option with jumps. First, we discuss the pricing of Russian options when the stock pays dividends continuously. Secondly, we derive the value function of Russian options by solving the ordinary differential equation with some conditions (the value function is continuous and differentiable at the optimal boundary for the buyer). And we investigate properties of optimal boundaries of the buyer. Finally, some numerical results are presented to demonstrate analytical properties of the value function.

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FIRST PASSAGE TIMES FOR RISK-TRACKING PROXIES

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024905003128 ◽

2005 ◽

Vol 08 (04) ◽

pp. 445-462

Author(s):

VICTOR VAUGIRARD

Keyword(s):

Interest Rates ◽

Rational Expectations ◽

Diffusion Processes ◽

First Passage Time ◽

Closed Form Solution ◽

Passage Time ◽

Form Solution ◽

First Passage ◽

Catastrophe Bonds ◽

Jump Diffusion Processes

This paper determines first passage time distributions with a two-fold emphasis. The focus is first set on interest rate randomness. It derives a closed-form solution in the case of moving boundaries, indexed on risk-free bonds, and where interest rates obey mean-reverting processes and underlyings follow lognormal diffusion processes. It turns next to the underlyings, which may not be exchange-traded and whose dynamics obey jump-diffusion processes. It builds an equilibrium valuation framework and determines the rational-expectations equilibrium price of digital options. As those underlyings may be risk-tracking indices, the article can be applied to pricing insurance-linked securities, such as catastrophe bonds.

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