A CLOSED-FORM GARCH VALUATION MODEL FOR POWER EXCHANGE OPTIONS WITH COUNTERPARTY RISK

2019 ◽  
Vol 34 (2) ◽  
pp. 279-296
Author(s):  
Xingchun Wang ◽  
Guangli Xu ◽  
Dan Li
Keyword(s):  
Closed Form ◽  
Default Risk ◽  
Reduced Form ◽  
Characteristic Functions ◽  
Counterparty Risk ◽  
Total Risk ◽  
Valuation Model ◽  
Power Exchange ◽  
Measure Change ◽  
Exchange Options

AbstractIn this paper, a discrete-time framework is proposed to value power exchange options with counterparty default risk, where counterparty risk is considered in a reduced-form setting and the variance processes of the underlying assets are captured by GARCH processes. In addition, the proposed model allows for the correlation between the intensity of default and the variances of the underlying assets by breaking down the total risk into systematic and idiosyncratic components. By dint of measure-change techniques and characteristic functions, we obtain the closed-form pricing formula for the value of power exchange options with counterparty default risk. Finally, numerical results are presented to show the power exchange option values.

Analytical valuation of power exchange options with default risk

2019 ◽  
Vol 28 ◽  
pp. 265-274 ◽  
Author(s):  
Guangli Xu ◽  
Xinjian Shao ◽  
Xingchun Wang
Keyword(s):  
Default Risk ◽  
Power Exchange ◽  
Exchange Options

The Valuation of Power Exchange Options with Counterparty Risk and Jump Risk

2016 ◽  
Vol 37 (5) ◽  
pp. 499-521 ◽  
Author(s):  
Xingchun Wang ◽  
Shiyu Song ◽  
Yongjin Wang
Keyword(s):  
Counterparty Risk ◽  
Jump Risk ◽  
Power Exchange ◽  
Exchange Options

A CLOSED-FORM PRICING FORMULA FOR EUROPEAN EXCHANGE OPTIONS WITH STOCHASTIC VOLATILITY

2021 ◽  
pp. 1-10
Author(s):  
Puneet Pasricha ◽  
Anubha Goel
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stochastic Volatility Model ◽  
Strike Price ◽  
Volatility Model ◽  
Exchange Options ◽  
Pricing Formula ◽  
Exchange Option

This article derives a closed-form pricing formula for the European exchange option in a stochastic volatility framework. Firstly, with the Feynman–Kac theorem's application, we obtain a relation between the price of the European exchange option and a European vanilla call option with unit strike price under a doubly stochastic volatility model. Then, we obtain the closed-form solution for the vanilla option using the characteristic function. A key distinguishing feature of the proposed simplified approach is that it does not require a change of numeraire in contrast with the usual methods to price exchange options. Finally, through numerical experiments, the accuracy of the newly derived formula is verified by comparing with the results obtained using Monte Carlo simulations.

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.

scholarly journals Estimation for Wrapped Zero Inflated Poisson and Wrapped Poisson Distributions

2016 ◽  
Vol 5 (3) ◽  
pp. 1 ◽  
Author(s):  
Aerambamoorthy Thavaneswaran ◽  
Saumen Mandal ◽  
Dharini Pathmanathan
Keyword(s):  
Closed Form ◽  
Information Matrix ◽  
Score Function ◽  
Function Approach ◽  
Closed Form Expression ◽  
Characteristic Functions ◽  
Model Parameters ◽  
Estimating Function ◽  
Method Of Moment ◽  
Poisson Distributions

There has been a growing interest in discrete circular models such as wrapped zero inflated Poisson and wrapped Poisson distributions and the trigonometric moments (see Brobbey et al., 2016 and Girija et al., 2014). Also, characteristic functions of stable processes have been used to study the estimation of the model parameters using estimating function approach (see Thavaneswaran et al., 2013). One difficulty in estimating the circular mean and the resultant mean length parameter of wrapped Poisson (WP) or wrapped zero inflated Poisson (WZIP) is that neither the likelihood of WP/WZIP random variable nor the score function is available in closed form, which leads one to use either trigonometric method of moment estimation (TMME) or an estimating function approach. In this paper, we study the estimation of WZIP distribution and WP distribution using estimating functions and obtain the closed form expression of the information matrix. We also derive the asymptotic distribution of the tangent of the mean direction for both the WZIP and WP distributions.

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