Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging

Yamada, Yuji; Primbs, James A.

doi:10.1007/s10690-005-9005-2

“…For the multinomial process we follow Yamada and Primbs (2004), Maller, Solomon and Szimayer (2006), and choose a step size and 2M jump sizes given by j for j = 1; ; M: The step size will be determined later. For the jump size x j = j ; y j = j we evaluate the arrival rates…”

Section: Multinomial Approximationsmentioning

confidence: 99%

Dynamic conic hedging for competitiveness

Madan

¹

,

Pistorius

²

,

Schoutens

³

2016

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The paper provides a new hedging methodology permitting systematic hedging choices with wide applications. Dynamic concave bid price, and convex ask price functionals from the recent literature are employed to construct new hedging strategies termed dynamic conic hedging. The primary focus of these strategies is to adopt positions maximizing a nonlinear conditional expectation expressed recursively as a concave current bid price for the one step ahead risk held or minimizing the convex current ask price for the risk promised. Risk management and hedging then have a new market value enhancing perspective di¤erent from the classical forms of risk mitigation, local variance minimization, or even expected utility maximization.

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“…Binomial three model and multinomial tree models, which have more than tree branches at each node, can be also defined in much the same way. The latter ones are useful approximation for a continuous stochastic model with higher moments [9].…”

Section: Solving the Msoh Problemmentioning

confidence: 99%

“…It is known that the more number of branches we take the more approximation accuracy we will obtain [9]. To see the efficiency of the NMSOH problem, two is enough.…”

Section: Numerical Examplesmentioning

confidence: 99%

See 1 more Smart Citation

Mean square optimal hedging with non-uniform rebalancing intervals

Sato¹,

Yamauchi

²

,

Fujioka³

2008

2008 SICE Annual Conference

0

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This paper proposes a method of discrete hedging by extending the MSOH (mean square optimal hedging) problem. In the proposed method, the risk of option sellers is minimized in terms of the mean square hedging error as in the MSOH problem, while it is allowed to rebalance with non-uniform intervals as opposed to the uniform assumption in the MSOH problem. The benefit of the extra freedom is demonstrated via numerical simulations.

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“…Another refinement for such problems, which is recently called the MSOH (mean square optimal hedging) problem, is proposed in, e.g, [5]- [7]. These results mainly improve computational algorithms.…”

Section: Introductionmentioning

confidence: 99%

Mean Square Optimal Hedging with Non-Uniform Rebalancing Intervals

Sato

¹

,

Yamada

²

,

Fujioka

³

2009

SICE Journal of Control, Measurement, and System Integration

Self Cite

0

View full text Add to dashboard Cite

This paper proposes a method of discrete hedging by extending the MSOH (mean square optimal hedging) problem. In the proposed method, the risk of option sellers is minimized in terms of the mean square hedging error as in the MSOH problem, while it is allowed to rebalance with non-uniform intervals as opposed to the uniform assumption in the MSOH problem. The benefit of the extra freedom is demonstrated via numerical simulations.

show abstract

Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging

Abstract: multinomial lattice, cumulants, excess kurtosis and skewness, compound poisson process, volatility smile,

Cited by 18 publications

References 37 publications

Dynamic conic hedging for competitiveness

Dynamic conic hedging for competitiveness

Mean square optimal hedging with non-uniform rebalancing intervals

Mean Square Optimal Hedging with Non-Uniform Rebalancing Intervals

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