scholarly journals Joshi’s Split Tree for Option Pricing

Risks ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 81
Author(s):  
Guillaume Leduc ◽  
Merima Nurkanovic Hot
Keyword(s):  
Closed Form ◽  
Numerical Study ◽  
Convergence Theory ◽  
Two Phase ◽  
Binomial Tree ◽  
Put Options ◽  
American Put Options ◽  
Binomial Trees ◽  
American Case ◽  
American Put

In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a “flexible” version of Joshi’s tree, and develop the corresponding convergence theory in the European case: we find a closed form formula for the coefficients of 1/n and 1/n3/2 in the expansion of the error. Then we define several optimized versions of the tree, and find closed form formulae for the parameters of these optimal variants. In a numerical study, we found that in the American case, an optimized variant of the tree significantly improved the performance of Joshi’s original split tree.

scholarly journals A Quasi-Closed-Form Solution for the Valuation of American Put Options

2020 ◽  
Vol 8 (4) ◽  
pp. 62
Author(s):  
Cristina Viegas ◽  
José Azevedo-Pereira
Keyword(s):  
Closed Form ◽  
Method Of Lines ◽  
Closed Form Solution ◽  
Form Solution ◽  
Option Value ◽  
Put Options ◽  
American Put Option ◽  
Put Option ◽  
American Put Options ◽  
American Put

This study develops a quasi-closed-form solution for the valuation of an American put option and the critical price of the underlying asset. This is an important area of research both because of a large number of transactions for American put options on different underlying assets (stocks, currencies, commodities, etc.) and because this type of evaluation plays a role in determining the value of other financial assets such as mortgages, convertible bonds or life insurance policies. The procedure used is commonly known as the method of lines, which is considered to be a formulation in which time is discrete rather than continuous. To improve the quality of the results obtained, the Richardson extrapolation is applied, which allows the convergence of the outputs to be accelerated to values close to reality. The model developed in this paper derives an explicit formula of the finite-maturity American put option. The results obtained, besides allowing us to quickly determine the option value and the critical price, enable the graphical representation—in two and three dimensions—of the option value as a function of the other components of the model.

scholarly journals The volatility target effect in investment-linked products with embedded American-type derivatives

2019 ◽  
Vol 16 (3) ◽  
pp. 18-28 ◽  
Author(s):  
Sergio Albeverio ◽  
Victoria Steblovskaya ◽  
Kai Wallbaum
Keyword(s):  
Numerical Study ◽  
Stochastic Volatility Model ◽  
Put Options ◽  
American Put Options ◽  
Lookback Options ◽  
Volatility Model ◽  
Target Strategy ◽  
Target Effect ◽  
Equity Index ◽  
American Put

Volatility Target (VolTarget) strategies as underlying assets for options embedded in investment-linked products have been widely used by practitioners in recent years. Available research mainly focuses on European-type options linked to VolTarget strategies. In this paper, VolTarget-linked options of American type are investigated. Within the Heston stochastic volatility model, a numerical study of American put options, as well as American lookback options linked to VolTarget strategies, is performed. These are compared with traditional American-type derivatives linked to an equity index. The authors demonstrate that using a Volatility Target strategy as a basis for an embedded American-type derivative may make any protection fees significantly less dependent of changing market volatilities. Replacing an equity index with the VolTarget strategy may also result in reducing guarantee fees of the corresponding protection features in a highly volatile market environment.

scholarly journals Pricing Perpetual American Put Options with Asset-Dependent Discounting

2021 ◽  
Vol 14 (3) ◽  
pp. 130
Author(s):  
Jonas Al-Hadad ◽  
Zbigniew Palmowski
Keyword(s):  
Value Function ◽  
Asset Price ◽  
Stopping Times ◽  
Martingale Measure ◽  
Put Options ◽  
American Put Options ◽  
Exact Calculations ◽  
Negative Exponential ◽  
American Put ◽  
The Value Function

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VAPutω(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is a discount function and E is an expectation taken with respect to a martingale measure. Moreover, we assume that the asset price process St is a geometric Lévy process with negative exponential jumps, i.e., St=seζt+σBt−∑i=1NtYi. The asset-dependent discounting is reflected in the ω function, so this approach is a generalisation of the classic case when ω is constant. It turns out that under certain conditions on the ω function, the value function VAPutω(s) is convex and can be represented in a closed form. We provide an option pricing algorithm in this scenario and we present exact calculations for the particular choices of ω such that VAPutω(s) takes a simplified form.

An Early-Exercise-Probability Perspective of American Put Options in the Low-Interest-Rate Era

2014 ◽  
Vol 35 (12) ◽  
pp. 1154-1172 ◽  
Author(s):  
Daniel Wei-Chung Miao ◽  
Yung-Hsin Lee ◽  
Wan-Ling Chao
Keyword(s):  
Interest Rate ◽  
Put Options ◽  
Early Exercise ◽  
American Put Options ◽  
American Put
Sign in / Sign up

Export Citation Format

Share Document