On the Term Structure of Futures and Forward Prices

Björk, Tomas; Landén, Camilla

doi:10.1007/978-3-662-12429-1_7

Cited by 37 publications

(63 citation statements)

References 17 publications

(23 reference statements)

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“…However, despite the similarity, this is not a standard change of numéraire because neither S I i ,t i (T i ) is the price of a traded asset nor is B I i ,t i (T i ) a portfolio of tradable assets. Similar measures may be found in Carr [4] and Björk and Landén [2] 2 .…”

Section: Generic Contractsupporting

confidence: 81%

Unifying exotic option closed formulas

Veiga

Wystup²,

Esquível³

2011

Rev Deriv Res

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Section: Generic Contractsupporting

confidence: 81%

Unifying exotic option closed formulas

Veiga

Wystup²,

Esquível³

2011

Rev Deriv Res

View full text Add to dashboard Cite

“…Let us assume that the risk free interest rate is constant in time. This hypothesis guarantees that the forward prices/rates variable t x , > 0 t , is a martingale under the risk-neutral measure (see [25] Proposition 3.1). That is in this case the risk neutral measure used to compute the option prices coincides with the "physical" measure used to describe the dynamics of t x , t v , > 0 t , defined implicitly by (1), (2), (3), (4), (5) with the absorbing barrier in zero imposed to the variable t x , > 0 t .…”

Section: The Series Expansion Of the Option Pricesmentioning

confidence: 93%

The SABR Model: Explicit Formulae of the Moments of the Forward Prices/Rates Variable and Series Expansions of the Transition Probability Density and of the Option Prices

Fatone¹,

Mariani²,

Recchioni³

et al. 2014

JAMP

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How to cite this paper: Fatone, L., et al. (2014) AbstractThe SABR stochastic volatility model with β-volatility β є (0,1) and an absorbing barrier in zero imposed to the forward prices/rates stochastic process is studied. The presence of (possibly) nonzero correlation between the stochastic differentials that appear on the right hand side of the model equations is considered. A series expansion of the transition probability density function of the model in powers of the correlation coefficient of these stochastic differentials is presented. Explicit formulae for the first three terms of this expansion are derived. These formulae are integrals of known integrands. The zero-th order term of the expansion is a new integral formula containing only elementary functions of the transition probability density function of the SABR model when the correlation coefficient is zero. The expansion is deduced from the final value problem for the backward Kolmogorov equation satisfied by the transition probability density function. Each term of the expansion is defined as the solution of a final value problem for a partial differential equation. The integral formulae that give the solutions of these final value problems are based on the Hankel and on the Kontorovich-Lebedev transforms. From the series expansion of the probability density function we deduce the corresponding expansions of the European call and put option prices. Moreover we deduce closed form formulae for the moments of the forward prices/rates variable. The moment formulae obtained do not involve integrals or series expansions and are ex-

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“…However, both the present model and the Nielsen and Schwartz (2004) model are special cases of the more general theory of affine term structures for forward and futures described by Bjork and Landen (2002). There are three important differences between our work and that of Nielsen and Schwartz (2004).…”

Section: Introductionmentioning

confidence: 93%

A Two-Factor Model for Commodity Prices and Futures Valuation

Ribeiro¹,

Hodges

2004

SSRN Journal

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This paper develops a reduced form two-factor model for commodity spot prices and futures valuation. This model extends the Gibson and Schwartz (1990)-Schwartz (1997) two-factor model by adding two new features. First the Ornstein-Uhlenbeck process for the convenience yield is replaced by a Cox-Ingersoll-Ross (CIR) process. This ensures that our model is arbitrage-free. Second, spot price volatility is proportional to the square root of the convenience yield level. We empirically test both models using weekly

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On the Term Structure of Futures and Forward Prices

Cited by 37 publications

References 17 publications

Unifying exotic option closed formulas

Unifying exotic option closed formulas

The SABR Model: Explicit Formulae of the Moments of the Forward Prices/Rates Variable and Series Expansions of the Transition Probability Density and of the Option Prices

A Two-Factor Model for Commodity Prices and Futures Valuation

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