Gaussian factor models futures and forward prices

Hyndman, Cody B.

doi:10.1093/imaman/dpm019

Cited by 11 publications

(18 citation statements)

References 28 publications

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“…We shall prove, independent of the construction already presented, that the FBSDE (12)-(13) provides another example. Similar to the results of Hyndman (2005Hyndman ( , 2007aHyndman ( , 2009 …”

Section: Connections Between Qtsms and Fbsdessupporting

confidence: 88%

“…According to Richter (2012) there are very few examples where explicit solutions to quadratic BSDEs are available. Obviously, the results of Hyndman (2005Hyndman ( , 2007aHyndman ( , 2009) provide examples. We shall prove, independent of the construction already presented, that the FBSDE (12)-(13) provides another example.…”

Section: Connections Between Qtsms and Fbsdesmentioning

confidence: 99%

“…While the dynamics of X are Gaussian, and hence a special case of those considered in Hyndman (2007bHyndman ( , 2009, the dynamics for Y differ due to the exponential quadratic form of the terminal condition. Nevertheless, following the methodology of Hyndman (2009) and the previous section we are able to prove the following result which gives an explicit solution to the coupled quadratic FBSDE (32)-(33).…”

Section: Since Y T = G(t T ) = S(t X T ) We Have the Following Bsdementioning

confidence: 99%

“…The first approach, and our main focus, is based on forward-backward stochastic differential equations (FBSDEs), which we henceforth refer to the FBSDE approach and was previously introduced in the context of ATSMs in Hyndman (2005Hyndman ( , 2007aHyndman ( , 2009. By first characterizing the factor process and bond price in terms of the solution of coupled nonlinear FBSDEs and then demonstrating existence, uniqueness, and explicit solutions of the the FBSDEs the pricing problem is solved.…”

mentioning

confidence: 99%

“…The second approach, which we briefly consider, is based on the stochastic flows method studied by Elliott and van der Hoek (2001), Grasselli and Tebaldi (2007), and Hyndman (2007bHyndman ( , 2009. This method gives a closed-form solution to the pricing problems for certain ATSMs.…”

mentioning

confidence: 99%

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Explicit Solutions of Quadratic FBSDEs Arising From Quadratic Term Structure Models

Hyndman

Zhou

2015

Stochastic Analysis and Applications

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We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to similar results on affine term structure models of Hyndman (Math. Financ. Econ. 2(2):107-128, 2009) due to the relationship between quadratic functionals of Gaussian processes and linear functionals of affine processes. Similar to the affine case a sufficient condition for the explicit solutions to hold is the solvability in a fixed interval of Riccati-type ordinary differential equations. However, in contrast to the affine case, these Riccati equations are easily associated with those occurring in linear-quadratic control problems. We also consider quadratic models for a risky asset price and characterize the futures price and forward price of the asset in terms of similar FBSDEs. An example is considered, using an approach based on stochastic flows that is related to the FBSDE approach, to further emphasize the parallels between the affine and quadratic models. An appendix discusses solvability and explicit solutions of the Riccati equations.

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Section: Connections Between Qtsms and Fbsdessupporting

confidence: 88%

Section: Connections Between Qtsms and Fbsdesmentioning

confidence: 99%

Section: Since Y T = G(t T ) = S(t X T ) We Have the Following Bsdementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Explicit Solutions of Quadratic FBSDEs Arising From Quadratic Term Structure Models

Hyndman

Zhou

2015

Stochastic Analysis and Applications

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A forward–backward SDE approach to affine models

Hyndman

2009

Math Finan Econ

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We consider factor models for interest rates and asset prices where the riskneutral dynamics of the factors process is modelled by an affine diffusion. We characterize the factors process and bond price in terms of forward-backward stochastic differential equations (FBSDEs), prove an existence and uniqueness theorem which gives the solution explicitly, and characterize the bond price as an exponential affine function of the factors in a new way. Our approach unifies the results, based on stochastic flows, of Elliott and van der Hoek (Finance Stoch 5: [511][512][513][514][515][516][517][518][519][520][521][522][523][524][525] 2001) with the approach, based on the Feynman-Kac formula, of Duffie and Kan (Math Finance 6(4): 1996), and addresses a mistake in the approach of Elliott and van der Hoek (Finance Stoch 5:511-525, 2001). We extend our results on the bond price to consider the futures and forward price of a risky asset or commodity.Keywords Affine models · Forward-backward stochastic differential equations · Stochastic flows · Bond price · Futures price · Forward price JEL Classification E43 · G12 · G13 Mathematics Subject Classification (2000) 60G35 · 60H20 · 60H30 · 91B28 · 91B70

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