The Analytics of Reset Options

Cheng, W. Allen; Zhang, Shuguang

doi:10.3905/jod.2000.319114

Cited by 39 publications

(41 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A discussion of options with reset feature occurs in Cheng and Zhang [2000]. An example is a reset call option where the strike price of the call is reset to the prevailing asset price on a predetermined reset date if the option is out of the money on that date.…”

Section: Options With Reset Featuresmentioning

confidence: 99%

See 1 more Smart Citation

Pricing Algorithms for Options with Exotic Path-Dependence

Kwok

Lau

2001

JOD

View full text Add to dashboard Cite

A mong the three popular classes of option pricing algorithms, latticebased methods (binomial and trinomial schemes) continue to enjoy great popularity due to their pedagogical appeal and ease of construction. A variant of the lattice-based method, called the forward shooting grid (FSG) method, has been successfully applied to price a wide variety of pathdependent options, like lookback options and Asian options.The FSG approach is characterized by an auxiliary state vector at each node on the lattice tree. The state vector is used to capture the path-dependent feature of the option contract, like the extreme value of the asset price achieved so far or the average value (geometric or arithmetic) of the asset prices.In construction of the FSG algorithm, unlike the finite-difference algorithms, it is not necessary to deal with the corresponding governing differential equation for the value of the exotic path-dependent option. For some types of path-dependent options, like the window Parisian option and the alpha quantile option considered here, it is not quite straightforward to explicitly derive the partial differential equation for the option value. In these cases, the FSG approach has an advantage over the finite-difference approach in construction of the option pricing algorithms. I. FORWARD SHOOTING GRID ALGORITHMThe FSG approach was pioneered by Hull and White [1993] and Ritchken, Sankarasubramanian, and Vijh [1993] for the pricing of American-and European-style Asian and lookback options. A more systematic framework of the FSG method is presented by Barraquand and Pudet [1996]. Forsyth, Vetzal and Zvan [1999] study the convergence of the FSG algorithm in the pricing of Asian options and show that convergence of the numerical solutions depends in an important way on the method of interpolation of the average asset values between the lattice nodes.

show abstract

Section: Options With Reset Featuresmentioning

confidence: 99%

“…The evaluation of the analytic pricing formula for this reset call option is 29.4138 (see Cheng and Zhang [2000]). The plot clearly reveals the linear rate of convergence in ∆t of the numerical option values to the value obtained from the analytic price formula.…”

Section: Options With Reset Featuresmentioning

confidence: 99%

Pricing Algorithms for Options with Exotic Path-Dependence

Kwok

Lau

2001

JOD

View full text Add to dashboard Cite

show abstract

“…Hsueh and Gou (1998), on the other hand, analyze the multiple reset feature that is included in most covered warrants traded in Taiwan. More recently, Cheng and Zhang (2000) discuss the pricing and hedging of reset options and propose a closed-form pricing formula for this increasingly popular derivative instrument.…”

Section: Introductionmentioning

confidence: 99%

Step‐reset options: Design and valuation

Hsueh

Liu

2001

Journal of Futures Markets

View full text Add to dashboard Cite

This study proposes a new design of reset options in which the option's exercise price adjusts gradually, based on the amount of time the underlying spent beyond prespecified reset levels. Relative to standard reset options, a step-reset design offers several desirable properties. First of all, it demands a lower option premium but preserves the same desirable reset attribute that appeals to market investors. Second, it overcomes the disturbing problem of delta jump as exhibited in standard reset option, and thus greatly reduces the difficulties in risk management for reset option sellers who hedge dynamically. Moreover, the step-reset feature makes the option more robust against short-term price movements of the underlying and removes the pressure of price manipulation often associated with standard reset options.To value this innovative option product, we develop a tree-based valuation algorithm in this study. Specifically, we parameterize the trinomial tree model to correctly account for the discrete nature of reset monitoring. The use of lattice model gives us the flexibility to price step-reset options with American exercise right. Finally, to accommodate the path-dependent exercise price, we introduce a state-to-state recursive pricing procedure to properly capture the path-dependent step-reset effect and enhance computational efficiency.

show abstract

“…Gray and Whaley [1999] also provided a closed-from solution for reset option with single reset date. Cheng and Zhang [2000] studied the reset options that the strike price will be reset to the prevailing stock price if the option is out of money. A closed-form pricing formula in terms of the multivariate normal distribution is derived under risk-neutral framework.…”

mentioning

confidence: 99%

“…A closed-form pricing formula in terms of the multivariate normal distribution is derived under risk-neutral framework. The terminal payoff of reset options with n reset dates and initial strike price 0 K , studied by Cheng and Zhang [2000], is as follows:…”

mentioning

confidence: 99%