Deriving derivatives of derivative securities

Carr, Peter

doi:10.1109/cifer.2000.844609

Cited by 13 publications

(15 citation statements)

References 21 publications

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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: 58%

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Unifying exotic option closed formulas

Veiga

Wystup²,

Esquível³

2011

Rev Deriv Res

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Section: Generic Contractsupporting

confidence: 58%

“…The approach we take to calculate the relevant partial derivatives relies on the works of Carr [4] and of Reiß and Wystup [17]. The first paper shows how to calculate spatial derivatives, i.e., derivatives with respect to the asset prices, by deriving the payoff function instead of the pricing formula.…”

Section: Derivativesmentioning

confidence: 99%

Unifying exotic option closed formulas

Veiga

Wystup²,

Esquível³

2011

Rev Deriv Res

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“…Avellaneda, Levy, and Paras (1995); Avellaneda and Paras (1996); and Avellaneda and Lewicki (1996) obtained pricing and hedging bounds in markets with bounds on uncertain volatility. Carr (1993) derived formulas for "the Greeks" associated with an option in a constant-coefficient market by differentiating the Black-Scholes equation. Martini (1995) has applied semigroup methods to the problem of misspecified volatility.…”

Section: Introductionmentioning

confidence: 99%

Robustness of the Black and Scholes Formula

Karoui

Jeanblanc‐Picquè

Shreve

1998

Mathematical Finance

342

247

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Consider an option on a stock whose volatility is unknown and stochastic. An agent assumes this volatility to be a specific function of time and the stock price, knowing that this assumption may result in a misspecification of the volatility. However, if the misspecified volatility dominates the true volatility, then the misspecified price of the option dominates its true price. Moreover, the option hedging strategy computed under the assumption of the misspecified volatility provides an almost sure one-sided hedge for the option under the true volatility. Analogous results hold if the true volatility dominates the misspecified volatility. These comparisons can fail, however, if the misspecified volatility is not assumed to be a function of time and the stock price. The positive results, which apply to both European and American options, are used to obtain a bound and hedge for Asian options.

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“…Since in the Black-Scholes universe P is a deterministic function of r, we have for This type of relations were already observed in a different context in Ref. [4]. Furthermore, Eq.…”

Section: Recovering Black-scholesmentioning

confidence: 69%

Local Scale Invariance and Contingent Claim Pricing

Hoogland

Neumann

2001

Int. J. Theor. Appl. Finan.

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Prices of tradables can only be expressed relative to one another at any instant of time. This fundamental fact should therefore also hold for contingent claims, i.e. tradable instruments, whose prices depend on the prices of other tradables. We show that this property induces a local scale invariance in the problem of pricing contingent claims.Due to this symmetry we do not require any martingale techniques to arrive at the price of a claim. If the tradables are driven by Brownian motion, we find, in a natural way, that this price satisfies a PDE. Both possess a manifest gauge invariance. A unique solution can only be given when we impose restrictions on the drifts and volatilities of the tradables, i.e. the underlying market structure. We give some examples of the application of this PDE to the pricing of claims. In the Black-Scholes world we show the equivalence of our formulation with the standard approach. It is stressed that the formulation in terms of tradables leads to a significant conceptual simplification of the pricing-problem.

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Deriving derivatives of derivative securities

Cited by 13 publications

References 21 publications

Unifying exotic option closed formulas

Unifying exotic option closed formulas

Robustness of the Black and Scholes Formula

Local Scale Invariance and Contingent Claim Pricing

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