Root’s barrier: Construction, optimality and applications to variance options

Cox, Alexander M. G.; Wang, Jiajie

doi:10.1214/12-aap857

Cited by 79 publications

(114 citation statements)

References 33 publications

(53 reference statements)

Supporting

Mentioning

113

Contrasting

Order By: Relevance

“…Hobson [33] in his pioneering work then showed how this can be used to compute model-independent prices and hedges of lookback options. Other exotic options were analysed in subsequent works; see Brown et al [12], Cox and Wang [18], Cox and Obłój [17]. The resulting no-arbitrage price bounds could still be too wide even for market making, but the associated hedging strategies were shown to perform remarkably well when compared to traditional delta-vega hedging; see Obłój and Ulmer [43].…”

Section: Short Literature Reviewmentioning

confidence: 99%

Robust pricing–hedging dualities in continuous time

Hou

Obłój

2018

Finance Stoch

View full text Add to dashboard Cite

We pursue a robust approach to pricing and hedging in mathematical finance. We consider a continuous-time setting in which some underlying assets and options, with continuous price paths, are available for dynamic trading and a further set of European options, possibly with varying maturities, is available for static trading. Motivated by the notion of prediction set in Mykland (Ann. Stat. 31:1413Stat. 31: -1438Stat. 31: , 2003, we include in our setup modelling beliefs by allowing to specify a set of paths to be considered, e.g. superreplication of a contingent claim is required only for paths falling in the given set. Our framework thus interpolates between model-independent and model-specific settings and allows us to quantify the impact of making assumptions or gaining information. We obtain a general pricing-hedging duality result: the infimum over superhedging prices of an exotic option with payoff G is equal to the supremum of expectations of G under calibrated martingale measures. Our results include in particular the martingale optimal transport duality of Dolinsky and Soner (Probab. Theory Relat. Fields 160:391-427, 2014) and extend it to multiple dimensions, multiple maturities and beliefs which are invariant under time-changes. In a general setting with arbitrary beliefs and for a uniformly continuous G, the asserted duality holds between limiting values of perturbed problems.

show abstract

Section: Short Literature Reviewmentioning

confidence: 99%

Robust pricing–hedging dualities in continuous time

Hou

Obłój

2018

Finance Stoch

View full text Add to dashboard Cite

show abstract

“…We next recall the recent work of Cox and Wang [14] and Gassiat et al [20]. For a function u : (t, x) ∈ R + × R −→ u(t, x) ∈ R, we denote by ∂ t u the t-derivative, Du, D 2 u the first and second spacial derivatives, i.e.…”

Section: Remark 26 Loynesmentioning

confidence: 99%

The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach

Cox

Obłój

Touzi

2018

Probab. Theory Relat. Fields

Self Cite

View full text Add to dashboard Cite

We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal argument. This approach allows us to address the long-standing question of a multiple marginals extension of the Root solution of the SEP. Our main result establishes a complete solution to the n-marginal SEP using first hitting times of barrier sets by the time-space process. The barriers are characterised by means of a recursive sequence of optimal stopping problems. Moreover, we prove that our solution enjoys a global optimality property extending the one-marginal Root case. Our results hold for general, one-dimensional, martingale diffusions. Mathematics Subject Classification

show abstract

“…This line of attack has been at the heart of the approach to robust pricing and hedging based on the Skorokhod embedding problem, as in [20,10,13,14,15]. It relies crucially on the ability to make a correct guess for the cheapest superhedge Y H,λ…”

Section: Optimal Transportation and Skorokhod Embedding Problemmentioning

confidence: 99%

“…This observation is the starting point of the seminal paper by Hobson [20] who exploited the already known optimality result of the Azéma-Yor solution to the SEP and, more importantly, provided an explicit static superhedging strategy. This methodology was subsequently used to derive robust prices and super/sub-hedging strategies for barrier options in Brown, Hobson and Rogers [10], for options on local time in Cox, Hobson and Ob lój [12], for double barrier options in Cox and Ob lój [13,14] and for options on variance in Cox and Wang [15], see Ob lój [32] and Hobson [21] for more details.…”

Section: Introductionmentioning

confidence: 99%

Maximum Maximum of Martingales Given Marginals

et al. 2012

View full text Add to dashboard Cite

We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset and statically trade European call options for all possible strikes and finitely-many maturities. We present a general duality result which converts this problem into a min-max calculus of variations problem where the Lagrange multipliers correspond to the static part of the hedge. Following Galichon, Henry-Labordère and Touzi [19], we apply stochastic control methods to solve it explicitly for Lookback options with a non-decreasing payoff function. The first step of our solution recovers the extended optimal properties of the Azéma-Yor solution of the Skorokhod embedding problem obtained by Hobson and Klimmek [22] (under slightly different conditions). The two marginal case corresponds to the work of Brown, Hobson and Rogers [9].The robust superhedging cost is complemented by (simple) dynamic trading and leads to a class of semi-static trading strategies. The superhedging property then reduces to a functional inequality which we verify independently. The optimality follows from existence of a model which achieves equality which is obtained in Ob lój and Spoida [33].

show abstract

Root’s barrier: Construction, optimality and applications to variance options

Cited by 79 publications

References 33 publications

Robust pricing–hedging dualities in continuous time

Robust pricing–hedging dualities in continuous time

The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach

Maximum Maximum of Martingales Given Marginals

Contact Info

Product

Resources

About