scholarly journals Option Pricing: Channels, Target Zones and Sideways Markets

2020 ◽  
pp. 25-33
Author(s):  
Zura Kakushadze
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Closed Form ◽  
Economic Environment ◽  
Target Zones ◽  
Long Period ◽  
Current State

After a market downturn, especially in an uncertain economic environment such as the current state, there can be a relatively long period with a sideways market, where indexes, stocks, etc., move in channels with support and resistance levels. We discuss option pricing in such scenarios, in both cases of unattainable as well as attainable boundaries, and obtain closed-form option pricing formulas. Our results also apply to FX rates in target zones without interest rate pegging (USD/HKD, digital currencies, etc.).

Bond valuation for generalized Langevin processes with integrated Lévy noise

2017 ◽  
Vol 18 (5) ◽  
pp. 541-563
Author(s):  
Alex Paseka ◽  
Aerambamoorthy Thavaneswaran
Keyword(s):  
Differential Equation ◽  
Parameter Estimation ◽  
Interest Rate ◽  
Option Pricing ◽  
Closed Form ◽  
Second Order ◽  
Option Prices ◽  
Interest Rate Models ◽  
Content Type ◽  
Bond Option

Purpose Recently, Stein et al. (2016) studied theoretical properties and parameter estimation of continuous time processes derived as solutions of a generalized Langevin equation (GLE). In this paper, the authors extend the model to a wider class of memory kernels and then propose a bond and bond option valuation model based on the extension of the generalized Langevin process of Stein et al. (2016). Design/methodology/approach Bond and bond option pricing based on the proposed interest rate models presents new difficulties as the standard partial differential equation method of stochastic calculus for bond pricing cannot be used directly. The authors obtain bond and bond option prices by finding the closed form expression of the conditional characteristic function of the integrated short rate process driven by a general Lévy noise. Findings The authors obtain zero-coupon default-free bond and bond option prices for short rate models driven by a variety of Lévy processes, which include Vasicek model and the short rate model obtained by solving a second-order Langevin stochastic differential equation (SDE) as special cases. Originality/value Bond and bond option pricing plays an important role in capital markets and risk management. In this paper, the authors derive closed form expressions for bond and bond option prices for a wider class of interest rate models including second-order SDE models. Closed form expressions may be especially instrumental in facilitating parameter estimation in these models.

PRICING VARIANCE SWAPS UNDER DOUBLE HESTON STOCHASTIC VOLATILITY MODEL WITH STOCHASTIC INTEREST RATE

2021 ◽  
pp. 1-17
Author(s):  
Huojun Wu ◽  
Zhaoli Jia ◽  
Shuquan Yang ◽  
Ce Liu
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Characteristic Functions ◽  
Stochastic Interest Rate ◽  
Modeling Framework ◽  
Variance Swaps ◽  
Volatility Model ◽  
Stochastic Interest

In this paper, we discuss the problem of pricing discretely sampled variance swaps under a hybrid stochastic model. Our modeling framework is a combination with a double Heston stochastic volatility model and a Cox–Ingersoll–Ross stochastic interest rate process. Due to the application of the T-forward measure with the stochastic interest process, we can only obtain an efficient semi-closed form of pricing formula for variance swaps instead of a closed-form solution based on the derivation of characteristic functions. The practicality of this hybrid model is demonstrated by numerical simulations.

The closed-form option pricing formulas under the sub-fractional Poisson volatility models

2021 ◽  
Vol 148 ◽  
pp. 111012
Author(s):  
XiaoTian Wang ◽  
ZiJian Yang ◽  
PiYao Cao ◽  
ShiLin Wang
Keyword(s):  
Option Pricing ◽  
Closed Form ◽  
Volatility Models
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