HKUST Institutional Repository
(5.016 recursos)
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Mostrando recursos 1 - 15 de 15
1.
Quanto lookback options - Kwok, Yue Kuen; Dai, Min; Wong, Hoi Ying
The lookback feature in a quanto option refers to the payoff structure where the terminal payoff of the quanto option depends on the realized extreme value of either the stock price or the exchange rate. In this paper, we study the pricing models of European and American lookback options with the quanto feature. The analytic price formulas for two types of European style quanto lookback options are derived. The success of the analytic tractability of these quanto lookback options depends on the availability of a succinct analytic representation of the joint density function of the extreme value and terminal value...
2.
Integral price formulas for lookback options - Xu, Chenglong; Kwok, Yue Kuen
We derive general integral representation of the price formulas for European options whose terminal payoff involves path dependent lookback variables. The intricacies in the derivation procedures using partial differential equation techniques stem from the degenerate nature of the pricing models, where the lookback state variables appear only in the auxiliary conditions but not in the governing differential equations. We also derive parity relation between the price functions of the floating strike and fixed strike lookback options.
3.
Valuing employee reload options under time vesting requirement - Dai, Min; Kwok, Yue Kuen
Upon the exercise of an employee stock option, the embedded reload provision entitles the holder to receive additional units of new options from the employer. The number of units of new options received is equal to the number of shares tendered as payment of strike and the new strike is set at the prevailing stock price. The reload provision may be subject to time vesting requirement, where the employee is prohibited from exercising the reload until the end of an initial vesting period. After each exercise, the new reload options are subject to the same time vesting constraint. In this...
4.
A tale of two options: employee reload options and shout call options - Dai, Min; Kwok, Yue Kuen
The reload provision in an employee stock option entitles its holder to receive one new (reload) option from the employer for each share tendered as payment of strike upon the exercise of the stock option. The number of reloads allowed can be finite or infinite. The shout feature in a call option allows its holder to reset the option's strike price to the prevailing stock price upon shouting. We examine the close relation between the employee reload options and shout call options. When the dividend yield of the underlying stock is zero, the value of the employee reload option can...
7.
A determinant condition from complex oscillation theory - Li, Kin-Yin
We give an explicit description of the solutions to the determinant condition on a third order complex linear differential equation studied by Chiang, Laine and Wang.
8.
Algebras associated with blaschke products of type g - Guillory, Carroll; Li, Kin-Yin
Let ? (resp. ?fi) be the set of all interpolating Blaschke products of (resp. finite) type G. Let E (resp. Efi) be the Douglas algebra generated by H? and the complex conjugates of elements of ? (resp. ?fi). Our main results are that the set of all invertible inner functions in E (resp. Efi) is the set of all finite products of elements of ? (resp. ?fi), which is also the closure of ? (resp. ?fi) among the Blaschke products. Consequently, finite convex combinations of finite products of elements of ? (resp. ?fi) are dense in the closed unit ball...
9.
American options with lookback payoff - Dai, Min; Kwok, Yue Kuen
We examine the early exercise policies and pricing behaviors of one-asset American options with lookback payoff structures. The classes of option models considered include floating strike lookback options, Russian options, fixed strike lookback options and pricing model of protection fund. In each class of the American lookback options, we analyze the characterization of the optimal stopping region, in particular, their asymptotic behaviors at time close to expiration and at infinite time to expiration. The inter-relations between the price functions of these American lookback options are explored. The mathematical technique of analyzing the exercise boundary curves of lookback options at infinitesimally...
10.
Optimal policies of call with notice period requirement for American warrants and convertible bonds - Dai, Min; Kwok, Yue Kuen
When an issuer calls its American warrant or convertible bond, the holder is usually given a notice period to decide either selling the derivative back to the issuer at the call price or exercising the conversion right. Several earlier papers have shown that such notice period requirement may substantially affect the optimal call policy adopted by the issuer. In this paper, we perform theoretical studies on the impact of the notice period requirement on issuer's optimal call policy for American warrants and convertible bonds. We also examine how the optimal call policy of the issuer interacts with holder's optimal conversion...
11.
Options with combinded reset rights on strike and maturity - Kwok, Yue Kuen; Dai, Min
Reset clauses on the strike price and maturity date are commonly found in derivative contracts, like insurance segregated funds, bonds and executive warrants. We analyze the optimal reset policy adopted by the holder of an option that possesses the reset rights on the strike price and date of maturity. The optimal reset policy relates closely to the temporal rate of change of the value of the new option received by the holder at the reset moment. The characterization of the optimal reset policy requires the solution of a free boundary value problem. As part of the solution procedure, we determine...
12.
On higher Frobenius-Schur indicators - Kashina, Yevgenia; Sommerhaeuser, Yorck; Zhu, Yongchang
We study the higher Frobenius-Schur indicators of modules over semisimple Hopf algebras, and relate them to other invariants as the exponent, the order, and the index. We prove various divisibility and integrality results for these invariants. In particular, we prove a version of Cauchy's theorem for semisimple Hopf algebras. Furthermore, we give some examples that illustrate the general theory.
13.
Self-dual modules of semisimple Hopf algebras - Kashina, Yevgenia; Sommerhaeuser, Yorck; Zhu, Yongchang
We prove that, over an algebraically closed field of characteristic zero, a semisimple Hopf algebra that has a nontrivial self-dual simple module must have even dimension. This generalizes a classical result of W. Burnside. As an application, we show under the same assumptions that a semisimple Hopf algebra that has a simple module of even dimension must itself have even dimension.
14.
Lattice points, Dedekind sums, and Ehrhart polynomials of lattice polyhedra - Chen, Bei-fang
Let ? be a simplex of RN with vertices in the integral lattice ZN. The number of lattice points of m? (= {m? : ? ? ?}) is a polynomial function L(?,m) of m ? 0. In this paper we present: (i) a formula for the coefficients of the polynomial L(?,t) in terms of the elementary symmetric functions; (ii) a hyperbolic cotangent expression for the generating functions of the sequence L(?,m), m ? 0; (iii) an explicit formula for the coefficients of the polynomial L(?; t) in terms of torsion. As an application of (i), the coefficient for the lattice...
15.
Valuation of employee reload options in utility maximization framework - Kwok, Yue Kuen; Lau, Ka Wo
The reload provision in an employee stock option is an option enhancement that allows the employee to pay the strike upon exercising the stock option using his owned stocks and to receive new 'reload' stock options. The usual Black-Scholes risk neutral valuation approach cannot be adopted as the pricing vehicle for employee stock options, due to the non-transferability of the ownership of the options and the restriction on short selling of the firm's stocks as hedging strategy. In this paper, we present a general utility maximization frmework to price non-tradeable employee stock options with reload provision. The risk aversion of...
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