Step‐reset options: Design and valuation

Abstract

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.

Analytics for geometric average trigger reset options

“…It is well-known that the delta jump problem makes hedging difficult for standard reset and barrier options. Modifications on standard reset and barrier options are therefore necessary to lessen the problem as surveyed in Hsueh and Liu (2002). The geometric average trigger reset option turns out not to have significant delta jumps.…”

Valuation on an Outside‐Reset Option with Multiple Resettable Levels and Dates

“…In their other paper (see Gray and Whaley [3]), they provided an explicit formula for the reset option with a periodic reset date. Hsueh and Guo [4], on the other hand, analyzed the multiple reset feature that is included in most covered warrants traded in Taiwan. More recently, Cheng and Zhang [5] discussed the pricing and hedging of reset options and propose a closedform pricing formula for this increasingly popular derivative instrument.…”

“…François-Heude and Yousfi [8] proposed a general valuation of reset option studied in Gray and Whaley [2] in which all options are replaced by ATM (At-The-Money) ones. Subsequent contributions include analytic extensions to multiple reset rights with shouting moment of Dai et al [9,10], Dai and Kwok [11], Yang et al [12], and Goard [13], step (or snapshot)-reset design of Hsueh and Liu [14], and Yu and Shaw [15], average trigger reset clauses of Kao and Lyuu [16], Liao and Wang [17], Kim et al [18], Chang et al [19], Dai et al. [20], and Costabile et al [21,22], window reset option with continuous reset constraints of Hsiao [23], and reset rights embedded in the Quanto options of Chen and Jiang [24].…”

“…For valuation on these options, one can look to Cheng and Zhang [5], Liao and Wang [17], Kim et al [18], Costabile et al [22], Zhang [28], and so forth. This paper is to discuss the pricing problem of the outside-reset option, defined by (2) and (4), and has two contributions. The first is to derive the analytical pricing formula for the outside-reset option under the proposed model.…”