On Approximate Pricing of Spread Options via Conditional Value-at-Risk

It is widely accepted to use conditional value-at-risk for risk management needs and option pricing. As a rule, there are difficulties in exact calculations of conditional value-at-risk. In the paper, we use the conditional value-at-risk methodology to price spread options, extending some approximation approaches for these needs. Our results we illustrate by numerical calculations which demonstrate their effectiveness. We also show how conditional value-at-risk pricing can help with regulatory needs inspired by the Basel Accords.

Correlating Lévy processes with self-decomposability: applications to energy markets

Based on the concept of self-decomposability, we extend some recent multidimensional Lévy models built using multivariate subordination. Our aim is to construct multivariate Lévy processes that can model the propagation of the systematic risk in dependent markets with some stochastic delay instead of affecting all the markets at the same time. To this end, we extend some known approaches keeping their mathematical tractability, study the properties of the new processes, derive closed-form expressions for their characteristic functions and detail how Monte Carlo schemes can be implemented. We illustrate the applicability of our approach in the context of gas, power and emission markets focusing on the calibration and on the pricing of spread options written on different underlying commodities.

Spread Option Pricing on Single-Core and Parallel Computing Architectures

This paper introduces parallel computation for spread options using two-dimensional Fourier transform. Spread options are multi-asset options whose payoffs depend on the difference of two underlying financial securities. Pricing these securities, however, cannot be done using closed-form methods; as such, we propose an algorithm which employs the fast Fourier Transform (FFT) method to numerically solve spread option prices in a reasonable amount of short time while preserving the pricing accuracy. Our results indicate a significant increase in computational performance when the algorithm is performed on multiple CPU cores and GPU. Moreover, the literature on spread option pricing using FFT methods documents that the pricing accuracy increases with FFT grid size while the computational speed has opposite effect. By using the multi-core/GPU implementation, the trade-off between pricing accuracy and speed is taken into account effectively.

Pricing and hedging tools for spread option contracts

This thesis examines the problem of pricing and hedging spread options under market models with jumps driven by a Compound Poisson Process. Extending the work of Deng, Li and Zhou we derive the price approximation for Spread options in jump-diffusion framework. We find that the proposed model accurately approximates option prices and exhibits reasonable behavior when tested for sensitivity to the model parameters. Applying the method of Lamberton and Lepeyre, we minimize the squared error between the Spread option price and the hedge portfolio to arrive to an optimal hedging strategy for discontinuous underlying price modes. Additionally, we propose an alternative average Delta-hedging strategy that is derived by conditioning the underlying price processes on the number of jumps and summing over all the possible jump combinations; such an approach allows us to revert to a hedging problem in a Black-Scholes framework. Although the average Delta-hedging strategy offers a significantly simpler approach to hedge Spread options, we conclude that the former strategy performs better by examining the Profit and Loss Probability Density Function of the two competing strategies. Finally, we offer a model parameter calibration algorithm and test its performance using the transitional Probability Density Functions.

Pricing and hedging tools for spread option contracts

This thesis examines the problem of pricing and hedging spread options under market models with jumps driven by a Compound Poisson Process. Extending the work of Deng, Li and Zhou we derive the price approximation for Spread options in jump-diffusion framework. We find that the proposed model accurately approximates option prices and exhibits reasonable behavior when tested for sensitivity to the model parameters. Applying the method of Lamberton and Lepeyre, we minimize the squared error between the Spread option price and the hedge portfolio to arrive to an optimal hedging strategy for discontinuous underlying price modes. Additionally, we propose an alternative average Delta-hedging strategy that is derived by conditioning the underlying price processes on the number of jumps and summing over all the possible jump combinations; such an approach allows us to revert to a hedging problem in a Black-Scholes framework. Although the average Delta-hedging strategy offers a significantly simpler approach to hedge Spread options, we conclude that the former strategy performs better by examining the Profit and Loss Probability Density Function of the two competing strategies. Finally, we offer a model parameter calibration algorithm and test its performance using the transitional Probability Density Functions.

Pricing spread options under Levy jump-diffusion models

This thesis examines the problem of pricing spread options under market models with jumps driven by a Compound Poisson Process and stochastic volatility in the form of a CIR process. Extending the work of Dempster and Hong, and Bates, we derive the characteristic function for two market models featuring normally distributed jumps, stochastic volatility, and two different dependence structures. Applying the method of Hurd and Zhou we use the Fast Fourier Transform to compute accurate spread option prices across a variety of strikes and initial price vectors at a very low computational cost when compared to Monte-Carlo pricing methods. We also examine the sensitivities to the model parameters and find strong dependence on the selection of the jump and stochastic volatility parameters.

Pricing spread options under Levy jump-diffusion models

This thesis examines the problem of pricing spread options under market models with jumps driven by a Compound Poisson Process and stochastic volatility in the form of a CIR process. Extending the work of Dempster and Hong, and Bates, we derive the characteristic function for two market models featuring normally distributed jumps, stochastic volatility, and two different dependence structures. Applying the method of Hurd and Zhou we use the Fast Fourier Transform to compute accurate spread option prices across a variety of strikes and initial price vectors at a very low computational cost when compared to Monte-Carlo pricing methods. We also examine the sensitivities to the model parameters and find strong dependence on the selection of the jump and stochastic volatility parameters.

Pricing spark spread options in electricity markets

This master's thesis develops a pricing method for spark spread options using a Monte Carlo method. The underlying commodities of interest, natural gas and uranium highlight the prevalence of natural gas power and nuclear power in Canada. To characterize the dynamics of electricity prices and capture specific features they have, two Levy models are proposed: a jump-diffusion model and a time-changed model. Real data are used to calibrate the models, using the daily average market prices for the last five years. We created a method to compute the price of the derivative under realistic modelling conditions using parameters found through the real data. Such models can be used to value the spark spread contracts to mitigate the risk associated the contracts.