Spread options, exchange options, and arithmetic Brownian motion

Purpose The purpose of this paper is to derive a new option pricing model for options on futures calendar spreads. Calendar spread option volume has been low and a more precise model to price them could lead to lower bid-ask spreads as well as more accurate marking to market of open positions. Design/methodology/approach The new option pricing model is a two-factor model with the futures price and the convenience yield as the two factors. The key assumption is that convenience follows arithmetic Brownian motion. The new model and alternative models are tested using corn futures prices. The testing considers both the accuracy of distributional assumptions and the accuracy of the models’ predictions of historical payoffs. Findings Panel unit root tests fail to reject the unit root null hypothesis for historical calendar spreads and thus they support the assumption of convenience yield following arithmetic Brownian motion. Option payoffs are estimated with five different models and the relative performance of the models is determined using bias and root mean squared error. The new model outperforms the four other models; most of the other models overestimate actual payoffs. Research limitations/implications The model is parameterized using historical data due to data limitations although future research could consider implied parameters. The model assumes that storage costs are constant and so it cannot separate between negative convenience yield and mismeasured storage costs. Practical implications The over 30-year search for a calendar spread pricing model has not produced a satisfactory model. Current models that do not assume cointegration will overprice calendar spread options. The model used by the Chicago Mercantile Exchange for marking to market of open positions is shown to work poorly. The model proposed here could be used as a basis for automated trading on calendar spread options as well as marking to market of open positions. Originality/value The model is new. The empirical work supports both the model’s assumptions and its predictions as being more accurate than competing models.

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Exchange options and spread options with stochastically correlated underlyings

Applied Economics Letters ◽

10.1080/13504851.2021.1907281 ◽

2021 ◽

pp. 1-9

Author(s):

Xingchun Wang

Keyword(s):

Spread Options ◽

Exchange Options

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Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

Journal of Applied Probability ◽

10.1017/s0021900200003041 ◽

2007 ◽

Vol 44 (02) ◽

pp. 393-408 ◽

Cited By ~ 1

Author(s):

Allan Sly

Keyword(s):

Stochastic Process ◽

Brownian Motion ◽

White Noise ◽

Gaussian Process ◽

Discrete Data ◽

Hölder Exponent ◽

Scaling Properties ◽

Multifractional Brownian Motion ◽

Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

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Brownian motion with quadratic killing and some implications

Journal of Applied Probability ◽

10.1017/s0021900200116079 ◽

1986 ◽

Vol 23 (04) ◽

pp. 893-903 ◽

Cited By ~ 2

Author(s):

Michael L. Wenocur

Keyword(s):

Brownian Motion ◽

Weibull Distribution ◽

Special Function ◽

Function Theory ◽

Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

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