A jump-diffusion model for pricing electricity under price-cap regulation

Abstract In this paper, we derive a new jump-diffusion model for electricity spot price from the “Price-Cap” principle. Next, we show that the model has a non-classical mean-reverting linear drift. Moreover, using this model, we compute a new exact formula for the price of forward contract under an equivalent martingale measure and we compare it to Cartea et al. (Appl Math Finance 12(4):313–335, 2005) formula.

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Pricing Participating Products under a Generalized Jump-Diffusion Model

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/2008/474623 ◽

2008 ◽

Vol 2008 ◽

pp. 1-30 ◽

Cited By ~ 26

Author(s):

Tak Kuen Siu ◽

John W. Lau ◽

Hailiang Yang

Keyword(s):

Diffusion Model ◽

Life Insurance ◽

Regime Switching ◽

Jump Diffusion ◽

Martingale Measure ◽

Practical Implementation ◽

Switching Models ◽

Jump Diffusion Model ◽

Equivalent Martingale ◽

Markovian Regime Switching

We propose a model for valuing participating life insurance products under a generalized jump-diffusion model with a Markov-switching compensator. It also nests a number of important and popular models in finance, including the classes of jump-diffusion models and Markovian regime-switching models. The Esscher transform is employed to determine an equivalent martingale measure. Simulation experiments are conducted to illustrate the practical implementation of the model and to highlight some features that can be obtained from our model.

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PRICING OF FIRST TOUCH DIGITALS UNDER NORMAL INVERSE GAUSSIAN PROCESSES

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024906003834 ◽

2006 ◽

Vol 09 (06) ◽

pp. 915-949 ◽

Cited By ~ 13

Author(s):

OLEG KUDRYAVTSEV ◽

SERGEI LEVENDORSKIǏ

Keyword(s):

Diffusion Model ◽

Diffusion Processes ◽

Jump Diffusion ◽

Spot Price ◽

Inverse Gaussian ◽

Jump Diffusion Processes ◽

Double Exponential ◽

Motion Approximation ◽

Jump Diffusion Model ◽

Normal Inverse Gaussian

We calculate prices of first touch digitals under normal inverse Gaussian (NIG) processes, and compare them to prices in the Brownian model and double exponential jump-diffusion model. Numerical results are produced to show that for typical parameters values, the relative error of the Brownian motion approximation to NIG price can be 2–3 dozen percent if the spot price is at the distance 0.05–0.2 from the barrier (normalized to one). A similar effect is observed for approximations by the double exponential jump-diffusion model, if the jump component of the approximation is significant. We show that two jump-diffusion processes can give approximately the same results for European options but essentially different results for first touch digitals and barrier options. A fast approximate pricing formula under NIG is derived.

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Pricing European-Style Options in General Lévy Process with Stochastic Interest Rate

Mathematics ◽

10.3390/math8050731 ◽

2020 ◽

Vol 8 (5) ◽

pp. 731

Author(s):

Xiaoyu Tan ◽

Shenghong Li ◽

Shuyi Wang

Keyword(s):

Interest Rate ◽

Diffusion Model ◽

Lévy Process ◽

Process Model ◽

Jump Diffusion ◽

Levy Process ◽

Martingale Measure ◽

Stochastic Interest Rate ◽

Stochastic Interest ◽

Jump Diffusion Model

This paper extends the traditional jump-diffusion model to a comprehensive general Lévy process model with the stochastic interest rate for European-style options pricing. By using the Girsanov theorem and Itô formula, we derive the uniform formalized pricing formulas under the equivalent martingale measure. This model contains not only the traditional jump-diffusion model, such as the compound Poisson model, the renewal model, the pure-birth jump-diffusion model, but also the infinite activities Lévy model.

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