scholarly journals Spread Option Pricing on Single-Core and Parallel Computing Architectures

2021 ◽  
Author(s):  
Shiam Kannan ◽  
Mesias Alfeus
Keyword(s):  
Fourier Transform ◽  
Option Pricing ◽  
Option Prices ◽  
Spread Options ◽  
Computational Performance ◽  
Computational Speed ◽  
The Difference ◽  
Spread Option ◽  
Short Time ◽  
Financial Securities

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.

ON SPREAD OPTION PRICING USING TWO-DIMENSIONAL FOURIER TRANSFORM

2019 ◽  
Vol 22 (05) ◽  
pp. 1950023
Author(s):  
MESIAS ALFEUS ◽  
ERIK SCHLÖGL
Keyword(s):  
Fourier Transform ◽  
Option Pricing ◽  
Closed Form ◽  
Stochastic Volatility Model ◽  
Approximation Formula ◽  
Two Dimensional ◽  
Spread Options ◽  
Variance Gamma Process ◽  
Volatility Model ◽  
Spread Option

Spread options are multi-asset options with payoffs dependent on the difference of two underlying financial variables. In most cases, analytically closed form solutions for pricing such payoffs are not available, and the application of numerical pricing methods turns out to be nontrivial. We consider several such nontrivial cases and explore the performance of the highly efficient numerical technique of Hurd & Zhou[(2010) A Fourier transform method for spread option pricing, SIAM J. Financial Math. 1(1), 142–157], comparing this with Monte Carlo simulation and the lower bound approximation formula of Caldana & Fusai[(2013) A general closed-form spread option pricing formula, Journal of Banking & Finance 37, 4893–4906]. We show that the former is in essence an application of the two-dimensional Parseval’s Identity. As application examples, we price spread options in a model where asset prices are driven by a multivariate normal inverse Gaussian (NIG) process, in a three-factor stochastic volatility model, as well as in examples of models driven by other popular multivariate Lévy processes such as the variance Gamma process, and discuss the price sensitivity with respect to volatility. We also consider examples in the fixed-income market, specifically, on cross-currency interest rate spreads and on LIBOR/OIS spreads.

Pricing spread options by generalized bivariate edgeworth expansion

2017 ◽  
Vol 04 (02n03) ◽  
pp. 1750017
Author(s):  
Edward P. C. Kao ◽  
Weiwei Xie
Keyword(s):  
Edgeworth Expansion ◽  
Price Difference ◽  
Empirical Estimation ◽  
Strike Price ◽  
Closed Form Solutions ◽  
Spread Options ◽  
Valuation Process ◽  
The Difference ◽  
Spread Option ◽  
Underlying Processes

A spread option is a contingent claim whose underlying is the price difference between two assets. For a call, the holder of the option receives the difference, if positive, between the price difference and the strike price. Otherwise, the holder receives nothing. Spread options trade in large volume in financial, fixed-income, commodity, and energy industries. It is well known that pricing of spread options does not admit closed-form solutions even under a geometric Brownian motion paradigm. When price dynamics experience stochastic volatilities and/or jumps, the valuation process becomes more challenging. Following the seminal work of Jarrow and Judd, we propose the use of Edgeworth expansion to approximate the call price. In the spirit of Pearson, we reduce the cumbersome computation inherent in Edgeworth expansion to single numerical integrations. For an arbitrary bivariate price process, we show that once its product cumulants are available, either by virtue of the structural properties of the underlying processes or by empirical estimation using market data, the approach enables analysts to approximate the call price easily. Specifically, the call prices so estimated capture the correlation, skewness, and kurtosis of the two underlying price processes. As such, the approach is useful for approximate valuations based on Lévy-based models.

scholarly journals Pricing Spread Options with Stochastic Interest Rates

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yunguo Jin ◽  
Shouming Zhong
Keyword(s):  
Option Pricing ◽  
Interest Rates ◽  
Stock Returns ◽  
Grid Method ◽  
Pricing Models ◽  
Stochastic Interest Rates ◽  
Spread Options ◽  
Asset Pricing Models ◽  
Stochastic Interest ◽  
Spread Option

Although spread options have been extensively studied in the literature, few papers deal with the problem of pricing spread options with stochastic interest rates. This study presents three novel spread option pricing models that permit the interest rates to be random. The paper not only presents a good approach to formulate spread option pricing models with stochastic interest rates but also offers a new test bed to understand the dynamics of option pricing with interest rates in a variety of asset pricing models. We discuss the merits of the models and techniques presented by us in some asset pricing models. Finally, we use regular grid method to the calculation of the formula when underlying stock returns are continuous and a mixture of both the regular grid method and a Monte Carlo method to the one when underlying stock returns are discontinuous, and sensitivity analyses are presented.

Improved Option Pricing Using Artificial Neural Networks and Bootstrap Methods

1997 ◽  
Vol 08 (04) ◽  
pp. 457-471 ◽  
Author(s):  
Paul R. Lajbcygier ◽  
Jerome T. Connor
Keyword(s):  
Neural Network ◽  
Option Pricing ◽  
Training Data ◽  
Stock Index ◽  
Option Prices ◽  
Hybrid Neural Network ◽  
Bootstrap Methods ◽  
Option Pricing Model ◽  
The Difference ◽  
Improved Performance

A hybrid neural network is used to predict the difference between the conventional option-pricing model and observed intraday option prices for stock index option futures. Confidence intervals derived with bootstrap methods are used in a trading strategy that only allows trades outside the estimated range of spurious model fits to be executed. Whilst hybrid neural network option pricing models can improve predictions they have bias. The hybrid option-pricing bias can be reduced with bootstrap methods. A modified bootstrap predictor is indexed by a parameter that allows the predictor to range from a pure bootstrap predictor, to a hybrid predictor, and finally the bagging predictor. The modified bootstrap predictor outperforms the hybrid and bagging predictors. Greatly improved performance was observed on the boundary of the training set and where only sparse training data exists. Finally, bootstrap bias estimates were studied.

scholarly journals Pricing spread options under Levy jump-diffusion models

2021 ◽  
Author(s):  
Matthew Cane
Keyword(s):  
Stochastic Volatility ◽  
Strong Dependence ◽  
Computational Cost ◽  
Compound Poisson Process ◽  
Model Parameters ◽  
Option Prices ◽  
Market Models ◽  
Spread Options ◽  
Spread Option ◽  
Cir Process

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.

scholarly journals Option Pricing And Monte Carlo Simulations

2011 ◽  
Vol 3 (9) ◽  
Author(s):  
George M. Jabbour ◽  
Yi-Kang Liu
Keyword(s):  
Monte Carlo ◽  
Option Pricing ◽  
Monte Carlo Simulations ◽  
Variance Reduction ◽  
Closed Form Solution ◽  
Form Solution ◽  
Price Convergence ◽  
Option Prices ◽  
Black Scholes ◽  
The Difference

The advantage of Monte Carlo simulations is attributed to the flexibility of their implementation. In spite of their prevalence in finance, we address their efficiency and accuracy in option pricing from the perspective of variance reduction and price convergence. We demonstrate that increasing the number of paths in simulations will increase computational efficiency. Moreover, using a t-test, we examine the significance of price convergence, measured as the difference between sample means of option prices. Overall, our illustrative results show that the Monte Carlo simulation prices are not statistically different from the Black-Scholes type closed-form solution prices.

A REGULARIZED FOURIER TRANSFORM APPROACH FOR VALUING OPTIONS UNDER STOCHASTIC DIVIDEND YIELDS

2010 ◽  
Vol 13 (02) ◽  
pp. 211-240 ◽  
Author(s):  
BAYE M. DIA
Keyword(s):  
Fourier Transform ◽  
Option Pricing ◽  
Inverse Fourier Transform ◽  
Option Price ◽  
Square Root ◽  
Option Prices ◽  
European Options ◽  
Dividend Yield ◽  
New Approach ◽  
Main Effects

This paper studies the option pricing problem in a class of models in which dividend yields follow a time-homogeneous diffusion. Within this framework, we develop a new approach for valuing options based on the use of a regularized Fourier transform. We derive a pricing formula for European options which gives the option price in the form of an inverse Fourier transform and propose two methods for numerically implementing this formula. As an application of this pricing approach, we introduce the Ornstein-Uhlenbeck and the square-root dividend yield models in which we explicitly solve the pricing problem for European options. Finally we highlight the main effects of a stochastic dividend yield on option prices.

scholarly journals Pricing spread options under Levy jump-diffusion models

2021 ◽  
Author(s):  
Matthew Cane
Keyword(s):  
Stochastic Volatility ◽  
Strong Dependence ◽  
Computational Cost ◽  
Compound Poisson Process ◽  
Model Parameters ◽  
Option Prices ◽  
Market Models ◽  
Spread Options ◽  
Spread Option ◽  
Cir Process

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 CMS SPREAD OPTIONS IN A LIBOR MARKET MODEL

2010 ◽  
Vol 13 (01) ◽  
pp. 45-62 ◽  
Author(s):  
DENIS BELOMESTNY ◽  
ANASTASIA KOLODKO ◽  
JOHN SCHOENMAKERS
Keyword(s):  
Numerical Study ◽  
Market Model ◽  
Approximation Methods ◽  
Option Prices ◽  
Model Assumption ◽  
Market Models ◽  
Libor Market Model ◽  
Spread Options ◽  
Swap Model ◽  
Spread Option

We present two approximation methods for the pricing of CMS spread options in Libor market models. Both approaches are based on approximating the underlying swap rates with lognormal processes under suitable measures. The first method is derived straightforwardly from the Libor market model. The second one uses a convexity adjustment technique under a linear swap model assumption. A numerical study demonstrates that both methods provide satisfactory approximations of spread option prices and can be used for calibration of a Libor market model to the CMS spread option market.

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