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 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 Pricing and hedging tools for spread option contracts

2021 ◽  
Author(s):  
Ekaterina Klyueva
Keyword(s):  
Probability Density ◽  
Option Price ◽  
Compound Poisson Process ◽  
Model Parameters ◽  
Hedging Strategy ◽  
Spread Options ◽  
Calibration Algorithm ◽  
Delta Hedging ◽  
Spread Option ◽  
Hedging Problem

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 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.

scholarly journals Pricing and hedging tools for spread option contracts

2021 ◽  
Author(s):  
Ekaterina Klyueva
Keyword(s):  
Probability Density ◽  
Option Price ◽  
Compound Poisson Process ◽  
Model Parameters ◽  
Hedging Strategy ◽  
Spread Options ◽  
Calibration Algorithm ◽  
Delta Hedging ◽  
Spread Option ◽  
Hedging Problem

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.

Capturing implied correlation skew from options prices via multiscale stochastic volatility models

2020 ◽  
Vol 07 (04) ◽  
pp. 2050042
Author(s):  
T. Pellegrino
Keyword(s):  
Stochastic Volatility ◽  
Calibration Procedure ◽  
Second Order ◽  
Model Parameters ◽  
Option Prices ◽  
European Options ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Order Expansion ◽  
Implied Correlation

The aim of this paper is to derive a second-order asymptotic expansion for the price of European options written on two underlying assets, whose dynamics are described by multiscale stochastic volatility models. In particular, the second-order expansion of option prices can be translated into a corresponding expansion in implied correlation units. The resulting approximation for the implied correlation curve turns out to be quadratic in the log-moneyness, capturing the convexity of the implied correlation skew. Finally, we describe a calibration procedure where the model parameters can be estimated using option prices on individual underlying assets.

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.

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 Option Pricing Driven by a Telegraph Process with Random Jumps

2012 ◽  
Vol 49 (3) ◽  
pp. 838-849 ◽  
Author(s):  
Oscar López ◽  
Nikita Ratanov
Keyword(s):  
Option Pricing ◽  
Financial Market ◽  
Option Prices ◽  
Martingale Measures ◽  
Market Models ◽  
Telegraph Process ◽  
Equivalent Martingale Measures ◽  
Hedging Strategies ◽  
Random Jumps ◽  
Equivalent Martingale

In this paper we propose a class of financial market models which are based on telegraph processes with alternating tendencies and jumps. It is assumed that the jumps have random sizes and that they occur when the tendencies are switching. These models are typically incomplete, but the set of equivalent martingale measures can be described in detail. We provide additional suggestions which permit arbitrage-free option prices as well as hedging strategies to be obtained.

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