This paper familiarizes the reader with contingent convertibles and their role in the current financial landscape. A contingent convertible is a security behaving like a bond in normal times, but that converts into equity or is written down in times of turbulence. The paper presents a few existing pricing approaches and introduces an extension to one of these, the equity derivatives approach, by letting the underlying asset follow a jump-diffusion process instead of a standard Geometrical Brownian Motion. The extension requires sophisticated computational techniques in order for the pricing to stay within reasonable time frames. Since market data is sparse and incomplete in this area, the validation of the model is not performed quantitatively, but instead supported by qualitative arguments.

Darbe nagrinėjami barjero pasirinkimo sandorių įkainojimo metodai. Barjero pasirinkimo sandorių išmokos sutampa su įprastinių pasirinkimo sandorių išmokomis, jei išpildoma papildoma barjero sąlyga, kurią reikia įvertinti. Įkainojimui naudojami diskretieji modeliai: binominis ir trinominis, tiriama jų konvergavimas į klasikinę Black-Scholes formulę. Dėl modelio diskretumo ir barjero sąlygos konvergavimas tam tikrais atvejais yra lėtas ir nemonotoniškas. Todėl siūloma pritaikyti adaptyviojo tinklelio algoritmą, smulkinant trinominio medžio tinklelį kritinėse srityse. Šiame darbe pateikiami rezultatai, gauti palyginus barjero pasirinkimo sandorio įkainojimo modelius. / In this paper we consider barrier options pricing models. Barrier options are standard call or put options except that they disappear or appear if the asset price crosses a predeterminant set of fixing dates. Barrier options are priced using continuous state Black-Scholes model and numerical approximation techniques, such as binomial and trinomial. Because of the the barrier condition and discreteness of these models the convergence to Black-Scholes model sometimes is slow. It is offered to apply adaptive mesh model grafting small sections of fine high-resolution lattice onto a tree in trinomial model. In this work we present the comparison of the models with some numerical results for barrier options.

本文目的在運用Adaptive Mesh Model，以具有高解析度的細網結構(fine mesh)來評價重設選擇權，以解決傳統Ritchken(1995) 樹狀模型在運用上會出現一些無法有效率運算和收斂狀況不佳二個問題。 本文的貢獻在發現評價重設選擇權可以使用下降生效界限選擇權的原理來探討。另外為解決上述Ritchken模型所面臨的二個問題，應用Adaptive Mesh Model於下生效界限選擇權，設置適當之細網結構，演算出更精確的重設選擇權價格。而且本樹網模型不再受限於美式下出界選擇權與美式下生效界限選擇權的組合不一定是美式重設選擇權的困擾。故在納入Adaptive Mesh Model的下降生效界限選擇權來評價歐式或美式重設選擇權，可以獲得良好的收斂效率。